The former Manchester United striker has not yet signed a a new deal, meaning the club may have to sell their star player or risk losing him for nothing in the summer.
The Whites have shown an interest in the Northern Ireland international and Shaw admits North End may have no option but to listen to offers.
Shaw said in the Lancashire Evening Telegraph: "David is at a good age, he is probably coming to a period where his best football will be played but he is an ambitious young man, a regular international and I think he wants to play on the bigger stage.
"He is definitely not trying to hold the club to ransom, it wasn't just about money for him although we have offered an extremely good contract to David and we very much want him to stay.
"We may be forced into having to take a much reduced offer for David, if that is what it comes to."