Black Cats boss
However, Press Association Sport understands it is the London side which has firmed up its interest.
Richardson was not included in the 18 for his side's Capital One Cup second-round victory over Morecambe, and O'Neill revealed the reason afterwards.
He said: "A club has made an offer for him today and we, as a club, have accepted that, and it gives Kieran the opportunity to find out for himself.
"If it doesn't materialise and he comes back, I'll still be pleased, but it's a position we might have to go and have a look at.
"Jack [Colback] played very, very well there tonight, but Kieran wanted to pursue this and have a look at this, finding we had accepted the offer, and I will see what comes of it."
It would come as no surprise if the former Manchester United player, who is in the final year of his contract, did leave the Stadium of Light after weeks of speculation over his future.
O'Neill has already been linked with a series of replacements, and he confirmed he would look to make progress on that front if a deal was to go through.
He said: "It is something, if Kieran does go, that we would have to look at."
Meanwhile, Fulham is on the brink of losing another star player in Moussa Dembele.
A club spokesperson confirmed a fee has been agreed with Tottenham Hotspur, which has also been given permission to hold talks with the Belgian midfielder.
With outcast Clint Dempsey seemingly on his way out of Craven Cottage to Sunderland, the loss of Dembele is another blow to manager Martin Jol, whose side crashed out of the Capital One Cup with a 1-0 defeat at Championship club Sheffield Wednesday.
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