Sam Allardyce is awaiting an answer from Lorient's Lamine Kone after Sunderland's on-off pursuit of the defender took a fresh twist.
Allardyce has twice ended his interest in Kone, 26, this month with the Black Cats initially cooling on a £5 million deal and then negotiations breaking down on the other side after a loan move had been proposed.
However, the transfer has been resurrected once again with Lorient vice-president Alex Hayes confirming that the club had received a bid they "couldn't refuse."
Hayes told Ouest France: "Sunderland have come back with a firm offer that we couldn't refuse. The ball is therefore in Lamine Kone's camp. He has to make his decision in the coming hours."
Allardyce has signalled his intention to bring in another defender and an attacking player before the end of the transfer window, having already signed Jan Kirchhoff, Dame N'Doye and Steve Harper.
Sunderland are also monitoring full-back Mathieu Debuchy's situation at Arsenal as he looks for regular club football ahead of this summer's Euro 2016, although they face a battle with fellow Premier League strugglers Aston Villa to strike a loan deal.
A successful swoop for Kone could see Sebastian Coates leave Wearside, with the former Liverpool defender understood to be the subject of talks with Portuguese club Sporting Lisbon.