Contract talks between Pearce and Royals have stalled, with the 23-year-old defender's current deal set to expire next summer.
Royals may now be forced to cash in during the January transfer window, with former manager Rodgers believed to be showing a strong interest.
Pearce was named Reading's Chronicle-sponsored Player of the Year last season, but has lost his place in the first team in recent weeks.
Royals boss Brian McDermott explained: "We spoke to Alex yesterday (Wednesday) so it's between him and the club now.
"I hope Alex stays and I would like him to sign. But January is approaching and if he hasn't signed we will see where we are."
Meanwhile, McDermott played down rumours linking the club with a move for Arsenal's out-of-favour Andrey Arshavin, 31, in January.
"He is not a Reading player and I won't comment on players at other clubs in the same division as us," he insisted.
Contract talks between Reading and striker Simon Church have also hit a deadlock.
The Wales international this week joined Huddersfield Town on loan for a month.