O'Leary was believed to be unhappy at suggestions the club might sell £30m-plus defender Rio Ferdinand and was sacked.
Keane starred at the World Cup finals for Ireland scoring three goals including last-gasp equalisers against Germany and Spain.
But he has struggled for firstteam football following the arrival of Robbie Fowler at Elland Road last November.
Sunderland have been seeking a new striker to replace Keane's Irish team-mate Niall Quinn, whose appearances have been limited by a back injury.
However, Sunderland's interest in Keane will have no effect on the future of Kevin Phillips, who has been linked with a possible move to several other clubs, including Tottenham.
Keane may be only 21 but has already cost clubs a staggering £31m. Manchester United manager Sir Alex Ferguson once claimed he would only pay £500,000 for the striker.
But other bosses have disagreedand Keane has already made three multi- million pound moves. In August 1999 Coventry paid Wolves £6m for the striker. Keane stayed at Highfield Road for a year before joining Inter Milan for £13m.
He only stayed at the Serie A club for five months before moving to Elland Road on loan. At the end of the 2000-2001 season, Leeds paid Inter £12m to make the deal permanent.
Italian club Parma today expressed surprise at reports suggesting O'Leary could be set for their top job because they have already appointed former Venezia coach Cesare Prandelli.
They dismissed the suggestion that the 44-year-old Irishman could be in place for the start of the new Serie A season, after reports that O'Leary had been approached in Sardinia.
Parma spokesman Giorgio Bottaro said: "We recently acquired a new coach, Cesare Prandelli, who was presented a month ago and has signed a two-year deal with us. We are not looking for a coach."
Meanwhile, Jose Antonio Camacho today resigned as Spain's national team coach after their disappointing World Cup, which saw them lose in the quarter-finals.
He had two years left on his contract but said: "I am 47 and I don't want to wait two years for the European Championships and another four years for the next World Cup."