The 25-year-old is currently a free agent after leaving Manchester United at the expiration of his latest deal following the conclusion of the 2022-23 season.
Tuanzebe spent the second half of last term on loan at Championship outfit Stoke City, however the defender's time in Staffordshire was blighted by injuries.
The centre-back featured only four times in the second tier for Alex Neil's, with the player's last full match coming on March 18 against Norwich City at the bet365 Stadium.
According to The Mirror, Tuanzebe could be set for another chance at Premier League football, with recently-promoted Luton Town interested in his services.
It is understood that the former Aston Villa loanee has agreed to join the Hatters on a trial period over the coming weeks in order to convince the club's hierarchy to offer him a permanent contract.
The report claims that Tuanzebe has been the target of clubs in the Saudi Pro League and Turkish Super Lig, with the former luring top European talent to the Middle East with lucrative contracts.
However, despite this interest from around the footballing world, it is believed that the centre-back wishes to remain in England and cement himself as a regular starter in the Premier League.
England's training base St George's Park has been Tuanzebe's home for the past three weeks, as the defender looked to build up his fitness following his departure from Old Trafford earlier in the summer.
Rob Edwards's men have already brought in 10 new signings in this transfer window as they hope to ensure their stay in the top flight is longer than a year, and the Hatters are starting to focus their recruitment on players who have experience in the Premier League.
Free agent Ross Barkley joined the club earlier this month to bolster Luton's midfield ranks, while 35-year-old goalkeeper Tim Krul will bring bags of top-flight knowhow from his time in net at Carrow Road.
A 4-1 defeat at the home of Europa League-bound Brighton & Hove Albion was a harsh welcome to the Premier League for Edwards's charges, and an intimidating trip to Stamford Bridge to face Chelsea is next up for the Hatters.
Luton started with a back three of Amari'i Bell, Mads Andersen and captain Tom Lockyer in their loss on the South Coast last weekend, when all three made their top-flight debuts.