According to Sky Sports, the two clubs are in discussions over a club record transfer fee for the Benin international.
Montpellier coach Michel Der Zakarian has claimed that Mounie was scheduled to undergo a medical in England on Monday.
"Steve Mounie has left. He will have a medical before signing in England," Der Zakarian said via Sky Sports.
Montpellier chief executive Laurent Nicollin added via Sky Sports: "Steve's case is an opportunity for him and for us."
The 22-year old scored 14 goals in 35 Ligue 1 appearances last season.