The 24-year-old was in strong form for his Dutch club during the 2021-22 campaign, scoring four times and registering four assists in 49 appearances in all competitions.
Sangare still has three years left to run on his current deal in Eindhoven, but there has been a host of speculation surrounding his future in recent weeks.
Leicester City have been credited with an interest in the Ivory Coast international, while Man United are believed to be keen to bring him to Old Trafford for the new campaign.
According to journalist Rudy Galetti, discussions between the Red Devils and PSV over a deal are 'progressing well and quickly', and there are 'positive feelings' on both sides.
Galetti claims that there is a release clause of €35m (£29.7m) in the contract of the midfielder, who started his professional career at Toulouse before moving to Holland.
Sangare, who largely operates as a defensive midfielder, has represented PSV on 87 occasions in all competitions, contributing five goals and six assists in the process.
Man United have already boosted their midfield this summer with the arrival of Christian Eriksen on a free transfer, while there have been claims that Lisandro Martinez, who is on the verge of joining the club from Ajax, could be used as a holding midfielder.
The Red Devils also continue to work on a deal for Frenkie de Jong but could be forced to abandon their pursuit of the Netherlands international if he continues to push to remain at Barcelona.
Man United lost both Paul Pogba and Nemanja Matic on free transfers over the summer, so they are currently short of experienced options in the middle of the park.
Scott McTominay and Fred are both expected to stay at the club this summer, while Charlie Savage and Zidane Iqbal have made positive impressions during their pre-season tour.
Savage and Iqbal could potentially head out on loan for the 2022-23 campaign, though, and it is unclear whether head coach Erik ten Hag is planning to keep hold of James Garner.
Garner, who spent the 2021-22 campaign on loan at Nottingham Forest in the Championship, is yet to play for Man United during their pre-season tour of Thailand and Australia due to injury.
Hannibal Mejbri was involved in Man United's first team towards the end of last season, but he has not been used in either of the team's friendlies against Liverpool and Melbourne Victory this summer.
The 20-time English champions have four more pre-season games this summer against Crystal Palace, Aston Villa, Atletico Madrid and Rayo Vallecano before starting their 2022-23 Premier League campaign at home to Brighton & Hove Albion on August 7.