The 28-year-old centre-back is available on a free transfer after leaving Burnley this summer, and interest has picked up sharply following a standout tournament with DR Congo, who reached the knockout stages of the World Cup for the first time before being narrowly beaten by England.
Tuanzebe made 16 appearances and scored once for Burnley last season as the club were relegated from the Premier League, having joined on a free transfer from Ipswich Town, where he had spent the two previous seasons.
Everton's interest is understood to be genuine, with David Moyes keen to add defensive depth as he looks to build on last season's mid-table finish and push for European qualification, while Brentford have also registered their own interest in the versatile defender, who can operate at centre-back or right-back.
Saudi Pro League clubs are also credited with interest and could offer Tuanzebe considerably more lucrative terms, though the former Manchester United academy product is said to be weighing his options carefully rather than rushing into a decision.
Since leaving Old Trafford in 2021, Tuanzebe's career has taken in loan and permanent spells at Aston Villa, Napoli, Stoke City, Ipswich and Burnley, and a return to regular Premier League football, even at a club not currently among England's elite, may prove the most appealing path for a player who impressed on the biggest stage this summer.