The 18-year-old was one of the key figures in Chelsea's youth sides who won the Uefa Youth League and the FA Youth Cup last season, and signed a four-year contract extension in March.
Musonda's father, Charly, a former midfielder for Anderlecht and Zimbabwe, believes that his son's development has been aided by training alongside Eden Hazard but says that a temporary move away from Stamford Bridge should be the next step.
"He must absolutely leave Chelsea and, since January, Monaco have been trying to sign him. Monaco are not alone but they truly want him,” Musonda senior told La Dernière Heure.
"He's not had a specific discussion with Jose Mourinho yet but he's trained regularly with the first team. He often watches his friend Eden Hazard. He plays an important role for Charly with his advice. My son does not want to copy his style but develop his own.
"Chelsea don't want him [to go back to Belgium]. They want Charly to play in a good team in a big league.
"He must play for a first team. He progresses every day but he must develop further. Technically, he's always been good but he still has much work to do on a physical and mental level. He's paying attention to this aspect of football.”