Bolton will double his wages to £30,000 a week if he pledges to stay.
Allardyce said: "There is no way we want to lose him as he is a very valuable player for us. But somebody can bid so much money that you cannot resist it."
In the event of Stelios leaving the Reebok this summer Bolton have already eyed a replacement in Inter Milan midfielder Andy van der Meyde.
Inter patron Massimo Moratti confirmed last week the Dutchman's future was in England and had been speaking with Tottenham and Everton about the winger.
But Bolton boss Sam Allardyce is also keen and will step up his bid should he lose Stelios to Liverpool.