The team wanted to reduce Jacobs' salary to create more cap flexibility. Jacobs said he was open to the idea as long as it was fair.
But they could not come to an agreement. Jacobs was due a $500,000 roster bonus in March to go along with the $4.4 million he was due this season.
Jacobs, the Giants' fourth-round pick in 2005, is fourth in franchise history with 4,849 rushing yards and has a franchise-record 56 rushing touchdowns.
Speaking to the New York Post, Jacobs said he thought he could play at least three more "good" years and that he hasn't ruled out joining the Jets despite a blunt -- and expressive -- postgame exchange this past season with coach Rex Ryan.
"I would love to do that,'' Jacobs told the newspaper. "It would be an opportunity for me to not have to relocate. I got to do what's best for my family. Whichever team it is, I think is going to be a lucky team. I got a lot left in me, got a lot to offer.''
Jacobs said he would have no problem getting along with Ryan.
"No question about it," Jacobs said. "There were a lot of things said in the heat of the battle. It's football. I talk with players on the other teams every week and shake their hand afterwards. I like Rex as a coach, I would definitely play for him. I would not say I wouldn't go there. It would be an opportunity to see how things are on the other side.''
"It's been a great ride," Jacobs said in a statement. "It's a great organization, a standup organization. I had fun. Won two Super Bowls here. I accomplished a lot in my career as a professional athlete here. That's it. It's been a good ride. Time to move on."
The team recently restructured Eli Manning's contract to create nearly $7 million in cap space.
"Brandon has truly been a great Giant," general manager Jerry Reese said in a statement. "These times are always very hard for me. We had a very good conversation today. We don't know what the future holds for Brandon, but we wish only the very best for him and his family."
"Brandon helped us win two world championships," Giants coach Tom Coughlin said in a statement. "He always did what was in the best interest of the team. No matter what you asked him to do, he performed and played in whatever role we asked him to perform. He really was a team player."