The 22-year-old enjoyed a productive campaign for Leverkusen from right-back, scoring eight goals and providing seven assists, double the amount he has managed in any other season of his young career.
Since making the switch from Scottish giants Celtic in January 2021, Frimpong has played 95 times for the BayArena club, scoring 11 goals, three of which were in the Europa League.
During an impressive season in terms of numbers from the Dutchman, he was able to help Xabi Alonso's men claim a place in the Europa League next term, finishing sixth in the Bundesliga standings.
According to the Manchester Evening News, Manchester United are yet to step up their efforts to bring Frimpong to Old Trafford following initial talks being held earlier in the window.
With two years left on the right-back's deal at the BayArena, it is understood that the arrival of the player to Erik ten Hag's squad would not come cheap.
The report adds that the Red Devils have approximately £120m to spend in this summer's transfer window, with £55m having already been used to lure Mason Mount away from Chelsea, wiping out a large chunk of the club's budget.
The England international ended a near life-long association with the Stamford Bridge club to join up with Three Lions teammates Marcus Rashford, Harry Maguire and Luke Shaw in Manchester.
With around £65m left to splash on transfers, it is believed that United are focusing on securing their primary targets before increasing their efforts to sign Leverkusen's Frimpong.
After the departure of David De Gea at the expiration of his contract, Ten Hag is looking to recruit Inter Milan goalkeeper Andre Onana to take the Spaniard's title of first-choice stopper.
It is said that Man United are hopeful that a deal for the Cameroonian stopper can be completed before the end of the week, although with four years left on his current terms at Inter, the 27-year-old does not represent a budget option.
United are also desperate to bring in a central striker following the expiration of Wout Weghorst's loan deal from Burnley, with Atalanta BC's Rasmus Hojlund high on the list of targets.
Arsenal have also been linked with a move for Frimpong this summer, although the Gunners are - according to Sky Sports News - planning to use Ajax defender Jurrien Timber at right-back should his transfer to the Emirates be completed.
A youthful Manchester United side got the club's pre-season fixtures up and running with a 2-0 victory over rivals Leeds United on Wednesday afternoon, with substitutes Joe Hugill and Noam Emeran netting their maiden goals for the first team.