Mandi, who has a year left on his contract, was relegated to Ligue 2 with Stade de Reims this past season.
Arsenal are reported to have scouted the 24-year-old earlier in the campaign, while Ligue 1 sides Rennes, Saint-Etienne and Bordeaux are now said to be courting him.
A natural right-back, Mandi could replace Ritchie de Laet, who has been on loan from Leicester City. However, he can play anywhere across the back four if required and spent much of the campaign at centre-half.
L'Equipe reports that Middlesbrough would like to move quickly on Mandi, as they look to add to their ranks following promotion.
Tomas Kalas could return to the Riverside next season, but fellow defenders Damia Abella and Jonathan Woodgate are set to depart the Riverside on free transfers.
Mandi scored five goals from 32 Ligue 1 appearances in 2015-16 and has been capped 23 times by Algeria, where his teammates include Premier League stars Riyad Mahrez, Nabil Bentaleb and Adlene Guedioura.