Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
Taylor was named club captain after signing from Watford in 2012 but has struggled to cement a spot in manager Dave Jones' first XI.
The 34-year-old was on loan at Brentford in September and is open to another move away from the Owls if he cannot reclaim a first-team place.
"It's not something I'd rule out (going out on loan), but it's the kind of thing that happens on a day-to-day basis in discussions with the manager," he told the Star.
"I enjoyed my time down there (Brentford) and managed to score a couple of goals. Getting the matches in is always good and it gets you fit.
"I've been in football long enough to know that things chance and I'm going to keep batting for my place."