England Under-21 international Ince turned in another eye-catching display as the Seasiders dispatched Blackburn 2-0 at the weekend.
The 20-year-old has 13 goals in 21 appearances this term and his form has sparked reports of interest from Manchester United and former club Liverpool.
"There have been no bids as far as I'm aware," Appleton told skysports.com. "I think there have been conversations with a couple of clubs and the chairman, but nothing concrete. No-one has come in yet and set the marker in terms of a price.
"To be fair to Tom, he's put it all to one side. He's just got on with his game and not let it affect him.
"He just has to keep on playing well for Blackpool. If he's got anything about him, he'll keep playing well and scoring for us. It's only fair for him and everyone else that he ignores the speculation.
"If the worst did happen in January, and we did lose Tom, then we have to make sure we have replacements ready. They will have to fill some very big shoes."