The 24-year-old defensive midfielder has been a first-team regular for the Dutch outfit since joining the club from Toulouse in September 2020, recording five goals and six assists in 88 games across all competitions.
Chelsea are understood to have identified Sanagre as a potential midfield target this summer, with the long-term futures of N'Golo Kante and Jorginho believed to be uncertain.
However, Sky Sports News claims that the Blues will face competition from Erik ten Hag's Man United for the Ivorian's signature.
The report adds that Sanagre is keen to move to England this summer and is convinced he will join a Premier League club ahead of the 2022-23 campaign.
The midfielder is also thought to have a €35m (£29.9m) release clause in his contract, which is due to expire in June 2025.
Sanagre, who has also been linked with Liverpool and Newcastle United, helped PSV defeat Ajax 2-1 to win the 2021-22 KNVB Beker.
Monaco 
Stade Brestois 29 
Bordeaux 
Nimes 
Bayern Munich 
FC Augsburg 
Paris Saint Germain 
Toulouse 
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen