Reports this week have suggested the former Manchester United midfiedler Richardson could be a January target for the Gunners, but the Black Cats are yet to receive any approach.
O'Neill said: "Arsenal have not been in touch with me, I don't know anything about it. I asked the chief executive as well and she said no, there hasn't been anybody in touch yet.
"But what I have said is that I would keep players informed about what is happening.
"Obviously, I don't want to rush players to leave the football club. I would rather think about stabilising things here, and hopefully we can try to progress from there.
"But regardless of whether you are going to be doing business or not, you are going to be linked with players, clubs are going to be linked with some of our players, and at this minute we are hanging in there.''
O'Neill has studiously avoided revealing his own recruitment plans for this month, insisting on the day he was unveiled that a transfer kitty was never discussed during his talks with owner and chairman Ellis Short.
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