Everton confirm Keane talks
Keane, 34, ended his 12-year association with United last month and is expected make a decision on his future by Monday.
Toffees boss Moyes would only tell Everton's website: "I can confirm we have had talks with Roy Keane."
But there are still several options open to the Irishman, not least of which is a potential a short-term deal alongside former United team-mate David Beckham at Real Madrid.
The former Irish international's advisors said that he would make his plans known early next week.
Michael Kennedy said: "We should know by Monday what is happening with Roy."
Kennedy said Keane has been keeping fit since leaving Old Trafford and will be ready to make a return to action in January after a broken foot.
But he declined to comment on reports that he has been in Madrid holding talks with Real about a move to La Liga, where a six month contract has been mooted.
West Bromwich Albion boss Bryan Robson - a former team-mate of Keane's - earlier confirmed he has spoken to Keane, who cannot sign a deal until January 1 next.
"I've spoken to Roy and he knows there is an option to come to this football club," Robson told the club's website.
"Roy has got loads of options available to him and within a few weeks he will make a decision on which challenge he wants. I've enquired about what he has in mind.
"But only Roy will be able to decide what that next challenge is going to be."
And last night, West Ham boss Alan Pardew said the club have made their case to coveted free agent Roy Keane, and are now awaiting his decision.
Since his dramatic exit from Old Trafford the inspirational midfielder has been the subject of frenzied transfer speculation, with a reported 40 clubs looking to sign him in January.
After putting their case to Keane, Pardew says he can now only wait for the much-desired midfielder to choose upon his final destination.
"I don't want to give too much away of what Roy wants to do but he knows we're there if his interest is strong for us," Pardew commented.
"We've just let it be known we're very interested in him, he'd be a great asset to our team and our club and it's up to him now to decide in his own time where his future lies."
As with the majority of clubs chasing Keane, West Ham will be unable to match the wages he commanded with The Red Devils, and the prospect of relocating to London may also not appeal to the star.
However, Pardew has made clear the club are willing to stretch their finances to lure the star.
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