Jones has been linked with a £5million move to the Stadium of Light, having also been tracked by Derby County.
Black Cats boss Keane is hoping to bring in more players before the close of the transfer window, but shied away from admitting an interest in Jones.
"I don't think it's fair to be commenting on players that we haven't been given permission to speak to," said Keane on Sky Sports News.
"I've said for weeks, and I will continue saying it, we are probably looking to add one or two players to the squad and that will continue over the next week or two.
"But I'd rather not comment on certain players at certain clubs because they're still under contract there."