The two clubs have reached agreement on a fee for the French 26-year-old and he looks set to be one of the first signings made by boss Paolo Di Canio, as he begins to re-shape the squad.
Everton and Liverpool have also been linked with Diakite, who fell out of favour somewhat at Lazio last season.
Signed from Pescara at the end of the 2005/06 season, Diakite has made 83 appearances for the Italian side, scoring twice.
Di Canio took over as Sunderland boss towards the end of the season and, having kept them in the top flight, now appears determined to revamp the squad he inherited from Martin O'Neill.
Young Altrincham striker Duncan Watmore has already been added to the development squad, and the Black Cats are also believed to be closing in on deals for Basle midfielder Cabral and Martimo defender Valentin Roberge.
Defence is likely to be a priority for Di Canio this off-season because Titus Bramble and Matt Kilgallon are due to formally part company with the club when their contracts expire at the end of the month, while loan signing Danny Rose has returned to Spurs.