Agent Shep Messing told the Daily Mail: "There is substance to reports of a Celtic interest but there are still a number of ifs and buts to be resolved."
Schwarzer admitted over the weekend he is not against a move to the SPL, saying: "All my options are open and I'm excited about the future. Will I stay in Britain, who knows? I'm up for anything.
"Right now, all the talk of Italy, Scotland or elsewhere is just speculation. I'm in good physical shape. I don't think my age is a deterrent for clubs. If anything these days, clubs seem to be leaning towards older keepers."