CALLUM McMANAMAN, who was linked with Celtic in the summer, is valued at over £4million by Wigan.
West Brom had a £3.5million bid rejected for the 23-year-old winger on Tuesday.
New Hawthorns boss Tony Pulis is now pondering upping the offer for the former Hoops target.
Pulis admitted he had made offers for “three or four players”.
He said: “You put them in and see what the clubs want.
“It’s not just McManaman, there are three or four other people we’ve enquired about.
“Then we’ll take a view about value for money and what is right for us.”
McManaman, part of Wigan’s 2013 FA Cup-winning side, is contracted to the club until 2017