"We have made an offer to Spurs for Mido," the Irish coach told the Daily Express on Monday.
The unsettled Mido was on the verge of joining Birmingham recently, but the deal fell through after the 24-year-old failed to agree personal terms with the Blues.
However, Keane is determined to capture the former Ajax forward, who persistently expressed his willingness to leave White Hart Lane after struggling to keep a regular place.
"He is a player I would like to speak to and to bring to this club. Trying to get these sorts of quality players is a challenge, but all I want is the opportunity to speak to the lad. If it doesn't work out then we will move on," he added.
The Black Cats have failed to sign any big names this summer in their attempts to reinforce the squad and be able to compete in the Premiership next season.