Will Grigg remains Sunderland's top striking target for the January transfer window.
The Black Cats launched a bid for the 27-year-old last week and have now returned with an increased offer.
Wigan boss Paul Cook said last week that he didn't want to lose the Northern Ireland international but he was an unused substitute as the Latics beat Aston Villa 3-0 on Saturday.
Grigg has struggled for regular football this season, scoring four goals in 18 appearances.
"It's hard in football, because for a manager to say 'nobody is for sale' would just be wrong," Cook said.
"But are we looking to sell players? Not a chance. Why would we?
"Will Grigg is one of the mainstays of what has brought me success at Wigan Athletic.
"You only need go back to the Manchester City game, and the only player to ever score a goal without a single team-mate in the same half as himself!
"I can't stop speculation, no-one can. I can't stop other clubs bidding for our players.
"But all I can is go on and on about partnerships...and for me, the Grigg and Powell partnership has been just fantastic.
"The front four partnership of Powell, Grigg, Jacobs, Massey is a proper front four.
"Will knows what I am waiting for, to get Will back in the team - the other three to be fit and available."
Jack Ross is keen to add a striker this month, and in particular an orthodox centre-forward.
"Charlie is our only number nine, really," Ross said last week.
“Josh likes to play in those little areas.
“So I think we need another type where everyone would say, ‘he’s a definite striker’.
“You’ve seen the importance of that in recent weeks I think, where we’re ahead in games or need to nick one, I think it would help us.”
Grigg is the obvious candidate having won promotion from the third tier on four separate occasions.
He scored 19 goals last season as Wigan stormed to the League One title and was the top scorer in the division back in 2015/16.
Sunderland's pursuit is unrelated to the future of Josh Maja, who is still yet to decide on his Black Cats future.
Maja missed the 1-1 draw with Luton Town on Saturday due to a stomach bug with his contractual situation unchanged.
Should he leave this month then Sunderland would go back into the market for further striking firepower.
Jack Ross said on Saturday that 'nothing was imminent' in terms of signing a new striker, but said that the club were working hard to try and boost his options as soon as possible.