The 31-year-old joined the MLS outfit ahead of the 2014 season, signing a four-year deal to remain as the club's designated player.
However, earlier this week president Tim Leiweke cast doubt over Defoe's future, with Varney adding fuel to the fire over speculation linking the striker with a move back to the Premier League in the New Year.
"In terms of Jermain in January, I don't know," FourFourTwo quotes the Reds boss as saying. "Maybe he comes back and he finds out that he really likes what's going on and the direction and he changes his mind.
"I have no idea where his mind's at, to be honest. I haven't had a sit-down, long conversation with him about things."
England international Defoe has previously enjoyed spells at West Ham United, Portsmouth and Tottenham Hotspur.