However, Press Association Sport understands speculation that the Black Cats have had a £5million bid for the player accepted by Russian side Zenit St Petersburg are wide of the mark.
The Wearside club have been tracking the Bruges-born 30-year-old as one of a series of potential targets, but their interest in him has to date not progressed beyond that point.
A former law student, Lombaerts has been at Zenit since 2007 and has made 240 appearances for the club.
Head coach Dick Advocaat made his first signing on Wednesday evening when the Black Cats completed a permanent deal for Liverpool defender Sebastian Coates, and he has signalled his intention to add quality, rather than quantity, to his squad this summer.
Advocaat dragged the club back from the brink of disaster during a nine-game cameo at the end of last season, but is convinced the club should be aiming higher than mere survival in the Barclays Premier League.
Source : PA
Source: PA