The Latics manager said: "If I go to my chairman with a suggestion of a name that would improve the squad then I'm sure he'd back me – whether it is Roy Keane or anybody else.
"I was very surprised when Manchester United let him leave as he's still a great player.
"He has a fantastic attitude on the field and everybody knows what a huge contribution he has made at Old Trafford during the past decade.
"However, I'm not going to say whether I'll be in for him or not – it's not something I've thought long and hard about.
"But I'm not ruling anything in or anything out.
"We've been thinking about improving the squad since the transfer window closed at the end of August, but we've eight Premiership fixtures before the end of December and a lot can change in that time.
"We could either be in the top three or in mid-table by then, so what happens in the next month will definitely influence my thoughts on who we should bring in.
"The chairman has backed me all the way in the transfer market, though, and if any transfer can be done that will improve the squad strength it will be done."
Keane's glorious career at United ended last Friday when Sir Alex Ferguson lost patience with a player whom he believed was beginning to destabilise the club.
But Lee McCulloch believes bringing Keane to the JJB Stadium would prove a
sensational signing.
The Latics midfielder said: "It would be brilliant having a player like Roy Keane at Wigan. Training with him every day would be incredibly special.
"It just shows how far Wigan have come that we are even getting linked with a name like Roy Keane.
"We've several young players in the squad and he might be the sort of personality we need to help and nurture them on the field in the future and it would raise the profile of Wigan ever further.
"Graham Kavanagh, who played alongside Roy in the Republic of Ireland team, said he is a lovely guy but everybody knows he is a winner with a phenomenal passion for the game.
"I certainly think Keane has two years left to play in the Premiership.
"Look at Teddy Sheringham – the guy is 39 and he's still doing a great job for West Ham United in the top flight.
"You are always trying to improve in this game and you'd learn so much from
having a guy like Roy Keane in the squad."
Latics have sold their 3,000 tickets for the Premiership date against Manchester United at Old Trafford on Wednesday, December 14.