The 27-year-old is out of contract after leaving Ligue 1 outfit Stade Rennais and is available on a free transfer.
He has been linked with Sam Allardyce’s side, along with the likes of Newcastle, Stoke City, West Bromwich Albion, French outfit Saint-Etienne and Bundesliga side Hamburg.
But Allardyce’s need for a left-back has cooled due to Patrick van Aanholt’s fine form last season, which saw the Dutchman sign a new contract earlier this month.
Allardyce is in the market for a full-back, but it is more a right-sided defender he wants with Sunderland looking to bring DeAndre Yedlin back to the Stadium of Light after his loan spell last season.
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That hasn’t stopped them being linked with M’Bengue, who is a man in demand given he won’t cost a transfer fee this summer.
And he says he would welcome a move to Wearside.
“It’s a club that interests me,” said M’Bengue. “All interest me.”
The defender’s agent has already opened talks with Hamburg, but the French-born star says he is in no rush to make a decision, though he wants his future sorted next month.
M’Bengue said: “It is true that I have a little attraction to the English league and the German championship.
“But there is also the reality of the market, supply and demand.
“I’m not focused on these championships. If I have something that fits me where the offer is interesting, why not...I am open to many things.
“Many clubs have approached me. Saint-Etienne asked me.
There is also Sunderland, clubs in Turkey, Newcastle. I will leave it a little time but not too much.”