The identity of the fourth team isn't known to the other clubs involved. But there is speculation among rival teams that the St. Louis Cardinals remain interested in the free-agent left-hander.
The Red Sox, Cubs and Giants were believed to be the last three teams still actively negotiating with Lester and his agents, Seth and Sam Levinson.
The Cardinals and Atlanta Braves, the other two clubs previously linked with Lester, had made public statements recently that appeared to downplay their interest.
However, teams pursuing Lester have suspected for some time that there were other clubs interested, the identity of which had never surfaced.
And Cardinals general manager John Mozeliak has never publicly commented about Lester specifically.
Mozeliak did tell the St. Louis Post-Dispatch last week that his team was "always open for business" and still exploring the free-agent pitching market in an "opportunistic" manner.
The Los Angeles Dodgers also have entered the mix, Boston radio station WEEI reported, citing multiple sources connected to teams interested in Lester.
On a conference call with reporters Tuesday night, Dodgers general manager Farhan Zaidi said the team's series of incremental moves so far, some of which were intended to bolster the team's Triple-A depth, could foreshadow bigger things.
"Having that base of depth gives you the opportunity to make more aggressive, needle-moving moves as the offseason goes on," Zaidi said.
Lester is described by clubs in the bidding as eager to finish the process and choose a team. He had hoped to sign before the winter meetings, which begin next week, but "that doesn't leave a whole lot of time," an executive of one team said.
Information from ESPN.com senior writer Jayson Stark and ESPNLosAngeles.com's Mark Saxon was used in this report.