The club refused to state Keane was on the brink of being handed the job, however they confirmed talks with "a high-profile figure" were ongoing with a view to a swift appointment.
The Black Cats slumped to a 2-0 defeat at Bury on Tuesday in the first round of the Carling Cup, a result which came on the back of four straight league losses.
Niall Quinn, the chairman-manager, decided to relinquish all coaching duties after the Gigg Lane shock and announced his intention to appoint a "world-class" new boss.
Manchester United legend Keane has no prior management experience, which would make him raw to the job rather than of established pedigree.
However he enjoyed enormous success during his playing career and as a former United captain is a recognised leader.
Quinn also knows him well, the pair having played in the same Republic of Ireland side for many years.
Sunderland said in a statement: "No new managerial appointment has been made at this time.
"The club is in discussions with a high-profile figure and is hopeful an announcement will be made in the near future."
Keane, 35, retired as a player in June, after a short spell with Celtic during which he helped the Bhoys win the Bank of Scotland Premier League and Scottish League Cup.
He ended a 12-year association with United in November 2005 and fulfilled a lifetime ambition by joining Celtic on an 18-month deal.
He managed only 13 appearances for the Hoops before quitting on medical advice.
With his body ravaged after cruciate ligament and hip operations, Keane had no choice other than to follow doctor's orders, and - should he be confirmed as Sunderland's new boss - there seems no prospect of him combining management with playing at the Stadium of Light.