Manager Martin Jol signed the 29-year-old free agent on a short-term contract in October after losing Mahamadou Diarra to injury.
Diarra, though, made a quick return from his knee problem and the recovery has left Tavares behind the Mali international and Chris Baird in Jol's plans.
But with Fulham facing 11 Premier League games before the end of 2012, the former Middlesbrough player could benefit from squad rotation.
"Tavares was a back-up player for me for Diarra and Chris Baird," said Jol in the Fulham Chronicle.
"There was not the situation where I could bring Tavares as well but hopefully he could be involved in the next couple of months."