Kurzawa has emerged as a summer transfer target for David Moyes, who is on the hunt for a long term replacement for Patrice Evra.
Moyes is planning a major squad overhaul in the summer, and is expected to be backed heavily in the transfer market as he looks to turn the club’s fortunes around.
Midfield reinforcements remain the priority, but Moyes is also looking to bring in defenders, with Nemanja Vidic joining Inter Milan, and the futures of Rio Ferdinand and Patrice Evra uncertain.
This has led to interest in Kurzawa, with Moyes sending scouts to watch him in action for Monaco this season.
The Frenchman has made 26 appearances for the Ligue 1 side this season.
The France Under-21 international admitted he would love the opportunity to join United, telling IN Sports: “The club of my dreams? Manchester United.
“It is one of my goals to play there one day.”