Ipswich boss Mick McCarthy has offered a short-term contract to former West Ham midfielder Jack Collison.
Chairman Fawaz Al Hasawi has vowed to strengthen Nottingham Forest year on year, with loan arrivals possible.
On Thursday, Appleton confirmed his chairman Karl Oyston and the Barclays Premier League club had held discussions about Ince, who left Anfield with one senior appearance to his name last summer, but the initial fee put forward fell short of Blackpool's valuation of the England Under-21 winger.
Ince was one of a number of Seasiders players frustrated by a goalkeeping masterclass from Carl Ikeme as Wolves left Bloomfield Road with a 2-1 npower Championship victory thanks to a goal in each half from striker Sylvan Ebanks-Blake.
Asked after the game whether Liverpool had upped their bid, Appleton said: "No, not that I'm aware of."
On Ince's impressive individual display, he added: "It was important for him and he's got to show a strength of character now to suggest that, with everything going on, all he wants to do is play football and play well for Blackpool Football Club."