But the Nigerian playmaker has made a dramatic return to form since the turn of the year and Bolton boss Allardyce admits the midfielder is making a strong case for a new deal.
He said: "In the form he is in at the moment, he is saying 'I'm here, I'm back and I want to play in the Premiership'.
"The offer from Qatar was huge but we rejected it in the end. Now we're seeing the form we knew he had.
"Jay-Jay is now back to his best and playing like we know he can and we are all very pleased to see that again."
Meanwhile, Wigan are being linked with a summer raid for Henrik Pedersen with reports claiming a £250,000 bid is on the cards.
Latics boss Paul Jewell was interested in bringing the Danish international to the JJB during the January transfer window but the move never came off and he is now considering making a fresh attempt to land him in the summer.