Ince left Anfield last summer after playing just once in the first team, with Blackpool paying just £250,000 in compensation
Liverpool boss Brendan Rodgers wants the forward - who has scored 13 goals in the Championship this season - back, and has made an offer for the 20-year-old.
But Appleton says the offer is nowhere near big enough for the hot prospect.
"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," he said.
"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 is a slight doubt for the weekend's game with Wolves but if fit Appleton said he will have no hesitation fielding him.
"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 (former England international Paul Ince) 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 a decent performance in.
"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."
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