The 25-year-old was again in impressive form for the Foxes during the 2021-22 campaign, scoring seven goals and registering five assists in 49 appearances in all competitions.
Tielemans's contract at the King Power Stadium is due to expire next summer, though, and he has been strongly linked with a move away from the club over the last few weeks.
Arsenal are said to be long-term admirers of the Belgium international, although the club's signing of Fabio Vieira has allegedly seen them cool their interest.
According to The Times, Tielemans is back on Man United's radar, with new Red Devils boss Erik ten Hag an admirer of the former Anderlecht youngster.
The 20-time English champions are said to be on the verge of signing Frenkie de Jong from Barcelona, with the two clubs believed to have now reached an agreement over the Netherlands international.
However, the departures of Paul Pogba and Nemanja Matic could lead to two central midfielders arriving at Old Trafford this summer, and Tielemans is said to have admirers at Old Trafford.
"That is not out of the question," Tielemans recently told reporters when questioned on a possible exit during this summer's transfer window. "I feel very good at Leicester, I was welcomed with open arms from day one. I give everything for the club until the last day.
"But of course you have to listen to other opportunities, you have to look at your career, and sometimes you have to make choices. Maybe one will come my way."
Tielemans is believed to be keen to play in the Champions League next term, but Man United will not be able to offer top-tier European action, having finished sixth in the Premier League table last season.
The Belgian joined Leicester from Monaco in January 2019, initially on loan, and he has been a vital player for the Foxes during his time at the club, scoring 24 goals and registering 24 assists in 157 appearances.
Tielemans scored six goals and registered four assists in 31 Premier League appearances last term, while he also featured eight times in the Conference League and five times in the Europa League.
Man United are also believed to be closing in on the signature of Feyenoord defender Tyrell Malacia, while a contract has allegedly been offered to experienced midfielder Christian Eriksen.
The Red Devils are also said to be keen to bring a new wide forward to the club, with Ajax's Antony thought to be a leading target during this summer's transfer window.
Man United will head off on their pre-season tour of Thailand and Australia on July 8, with their first friendly of the summer coming against Liverpool on July 12.