The 20-year-old was subject to a bid from his former employers a fortnight ago but the Seasiders manager has made clear that they need to improve their pay package
The 20-year-old has been in fine form for the Championship side this season, scoring 13 goals in 24 games, prompting interest from the club he left 18 months ago.
Goal.com revealed on Saturday that Liverpool is close to reaching an agreement with Blackpool over a fee for the winger, and Appleton has called on the Reds to up their offer if they wish to land the England Under-21 international.
"They [Liverpool] made an offer two weeks or so ago, we haven’t received anything else since," Appleton told reporters.
"It’s not enough, it’ll need to be better to secure the service of Tom and until that changes he’ll stay here.
"Why would any manager want to sell and get rid of his best players? I’d love to keep Tom.
"Everyone has got a price but we want to keep our best players and add to them and have a right go in the league."