Fisher is scheduled to clear waivers at 6 p.m. ET Wednesday. One source with knowledge of the talks told ESPN.com that Fisher is "very close" to committing to sign with the Thunder once he becomes a free agent.
ESPN.com reported Monday the Thunder and the Miami Heat had emerged as the two frontrunners to sign Fisher, who was officially released Monday night by the Houston Rockets after securing a buyout from Houston in the wake of last week's trade that brought an end to Fisher's second stint with the Los Angeles Lakers.
Sources told ESPN.com the Heat have made a strong recruitment effort to sign Fisher, but the Thunder have more financial flexibility to sign him and more of a role to offer after the loss of backup point guard Eric Maynor in early January to a season-ending knee injury. There also is a feeling among some rival teams that Fisher prefers to stay in the West, where he has played his entire career.
If the deal goes through, as expected, Fisher potentially will face the Lakers twice during the regular season at Staples Center (March 29 and April 22) before the playoffs.
At the morning shootaround before Tuesday night's game against the Utah Jazz, Durant strongly endorsed the prospect of signing Fisher to The Oklahoman, telling the newspaper: "Derek is a consummate professional ... an unbelievable leader. And he played with arguably one of the greatest players to ever play in Kobe (Bryant), and Kobe really respected him as a player and wanted him on his team, so that speaks volumes."
"We have a great corps of point guards leading off with Russ (Russell Westbrook) and then Reggie (Jackson) and Royal (Ivey)," Durant continued. "But adding another guy that can come in and give us some good minutes here and there and bring his leadership and winning plays here would be cool. But it's one of those things that you really don't know too much about. We got to just see what happens. (Fisher) is a Thunder guy as far as character and off the court is concerned. But we'll see what happens."
With the Chicago Bulls needing another big man more than another guard and the San Antonio Spurs still hopeful they can complete the signing of a guard by week's end, Oklahoma City and Miami emerged Monday as the two most likely landing spots for the 16-year veteran.
The Heat explored the possibility of signing Fisher when he was a free agent in the summer of 2010 and have strong interest now, sources say, even if they are successful in signing veteran forward Ronny Turiaf this week. Miami has only one open roster spot at present, but rookie shooting guard Terrel Harris hasn't played in six weeks and thus looms as a potential candidate to make way if the Heat need to make room for two signings.
Sources say the thought of signing with the Bulls is something that strongly interested Fisher, but Chicago is well stocked at point guard and appears to be focused on trying to land a forward such as Turiaf. The Los Angeles Clippers, sources say, have likewise shown little interest in pursuing Fisher, even though the Clippers -- like Miami and Oklahoma City -- have a need for a playoff-tested guard after Chauncey Billups' season-ending Achilles tear and with star guard Chris Paul carrying an increasingly heavy load.
The Spurs, by contrast, long have been fans of Fisher, sources said. But San Antonio, by all indications, is pressing ahead on the Patrick Mills front in hopes of completing its planned signing of the Australian point guard, who spent much of this season playing in China.
Fisher was officially placed on waivers at 6 p.m. ET Monday, giving teams under the salary cap 48 hours to claim him. He was owed a little less than $1 million for the rest of this season and had a player option worth $3.4 million for next season. But the Houston Chronicle reported Monday that Fisher surrendered his entire 2012-13 salary to secure his buyout from the Rockets.
Players seeking buyouts this month must be waived by Friday to be eligible to play in the playoffs with another team.
Fisher's surrender of next season's $3.4 million marks the second time in his career that he has left a significant amount of money on the table to facilitate a move he wants. In 2007, Fisher gave up roughly $8 million owed by the Utah Jazz to return to the Lakers -- with whom he began his career alongside Bryant in 1996-97 -- so Fisher's family could be closer to the doctors who were treating his daughter for a rare form of eye cancer.
The Rockets gave Fisher's representatives permission to speak with about a half-dozen teams over the weekend to gauge interest in him during the buyout discussions, sources said.
Fisher has made no public statements since his surprising trade from the franchise with which he has been a part of five championship teams. Lakers general manager Mitch Kupchak has admitted that he didn't give Fisher or his representatives a heads up that a deal was in the works before Thursday's trade deadline, and said later that he could understand if Fisher was "emotional" over the situation.
"He may have caught wind of the rumor a day or two ago, but there was no heads up given," Kupchak said Thursday. "It's not necessary, because a lot of times there's nothing to the rumors. How many times was one of our players traded in the last 10 days and it never took place? So you can't spend your time dispelling or confirming rumors.
"But when something like this does happen, I can imagine what he's going through. I've never really gone through it, but to be in one place, to have the kind of contribution, midseason, it's got to be pretty emotional. We'll talk at the right time."
Once he clears waivers, Fisher is free to sign with any team except the Lakers because league rules prevent teams from trading players away and immediately re-signing them.
Fisher had played in 537 consecutive games prior to being dealt to the Rockets. They had acquired him Thursday afternoon with the hopes of convincing Fisher to stay with them the remainder of the season, largely because star point guard Kyle Lowry is still recovering from a bacterial infection.
The Rockets, though, ultimately decided not to oppose Fisher's wish to be set free thanks to Fisher's willingness to give up next season's player option and that Houston also landed Dallas' 2012 protected first-round pick from the Lakers, which L.A. had acquired in December as part of the Lamar Odom deal.
Ramona Shelburne of ESPNLosAngeles.com and ESPN.com's Brian Windhorst contributed to this report.