The London-born 27-year-old, who played 90 minutes at left-back during the Black Cats' 0-0 draw with Arsenal on Saturday, is believed to be keen on a return to the capital.
"Kieron came to see me a while ago in the last transfer window. For family issues and things, he thought there maybe needed a change," said O'Neill.
"No-one has come in and made an offer. That, though, does not mean there is nothing happening, I just don't know.
"But if he performs like he did against Arsenal, I would like to keep him."