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The striker, a known favourite of Dons boss Jimmy Calderwood, had his contract with Boston Utd terminated "by mutual consent" after receiving treatment for an alcohol problem.
However, with Calderwood playing Scott Severin up front against Celtic last weekend, it may not be outwith the bounds of possibility that Whelan could tie up a short-term deal at the Dons.
Calderwood told the Press & Journal: "I have spoken to Noel and he has decided not to accept the offer from Livingston.
"We've agreed he can come and train with us, but there is no contract on offer.
"It will be a massive lift for everyone in the dressing-room because he was a big influence when he was with us last season. I'm looking forward to having him around - it will be nice to see his mischievous smile again."
"There's no doubt we have missed his bubbly character since he's been away, so from that point of view it will be good for us to have him with us."
Livingston boss John Robertson said last week that Whelan's agent priced him out of a move to Almondvale after the Lego club made Noel an offer based on appearances after a short trial period.
Robertson said: "Noel was very enthusiastic. Unfortunately his agent feels he is worth nearly double what we can afford to offer him.
31-year-old Whelan began his career with Leeds United then moved to Coventry, Middlesbrough, Millwall and Derby County before spending last season with Aberdeen.
He scored only 5 goals in a difficult injury-interrupted spell but helped Darren Mackie to his highest goals total at the club.