The 20-year-old is thought to have been in discussions with the Blues over an improved deal in recent weeks, having worked his way into first-team contention this season.
In a post on image-sharing social network Instagram on Monday night, the youngster posted a plain black picture alongside the message: "You sacrifice, you work hard, harder, you give more than what's expected, and often more than you can, because you love what you do and clearly more than you should.
"And what do you get back? Literally nothing,... done. However, with this being said I will continue with same dedication and commitment to this great game."
Musonda joined the Chelsea youth academy from Anderlecht in 2012 and spent the first half of last season out on loan with La Liga side Real Betis, where he scored once in 24 league appearances.