Ince left Anfield last summer having made one senior appearance, with Blackpool making a compensation payment of £250,000. The 20-year-old son of former England international Paul will command a far higher fee if he returns to Merseyside in January having netted 13 goals in 21 npower Championship games this season.
Speaking ahead of Friday night's home game with Wolves, Appleton told BBC Radio Lancashire: "As far as I'm aware I think there's been a conversation between Karl (Oyston) and Liverpool regarding an offer but, as far as I'm aware, it's way below the type of money we'd expect for someone of Tom's talent."
Appleton added: "Obviously the chairman keeps me informed but I think it was just an initial conversation between himself and Liverpool and there was a figure used but obviously it's way below, like I say."
Ince, who also netted eight times as the Seasiders reached the play-off final last term, is battling to overcome a slight hamstring strain in time to face Wolves and Appleton was defiant when asked whether he would play his star man if passed fit.
"Without a shadow of a doubt," he said.
"I wouldn't worry about that. And he'll continue to play as long as we hold his registration. He's quite a down to earth, sensible young lad anyway.
"I think having someone like his dad in his family who's been a professional footballer himself and knows the ups and downs of the game, I'm sure he'll put in a decent performance in."
Appleton added: "I wouldn't say I'm resigned to losing him just yet though. There's still a lot of work to be done before anything like that happens."
Source: PA
Source: PA