Since joining from Montrose in 2011, the 22-year-old has impressed for Alan Archibald's side, with Southampton, Leeds United and Birmingham City also reported to be keeping tabs on him.
Despite Celtic's interest, Taylor-Sinclair insists that he is concentrating on helping his current team, Thistle, who are currently ninth in the Scottish Premiership.
"Celtic have made contact with my agent but that is all I know," he told the Sunday Mail.
"For now, I'm focusing on Partick. It's only December and anything can happen.
"When the time comes, I'll have a serious think about things.
"It's good teams are showing an interest - it gives me confidence - but I must react to the speculation in a positive way."
Taylor-Sinclair also admitted that if he was to make the switch to Celtic Park, he would like to return to the Firhill Stadium in a loan capacity.
"The best scenario is that Thistle get some money in January then I'm loaned back here until the end of the season," he said.
"The fans see that I give 100 per cent. I love it here. I've been here for three years and they gave me a chance for which I'm grateful.
"I wouldn't say it's certain I won't be here next season. But I need to see how it goes.
"The gaffer has been great with me. I've played every single minute since he took over and hopefully that will continue."