The Blues have decided to loan the midfielder out for the remainder of the season, sparking a scramble to acquire his services.
The Telegraph claims Bournemouth, Watford, Newcastle and West Brom are all keen to snap up the Belgian ace this month.
Ross Barkley's arrival at Stamford Bridge in a £15m deal from Everton means Musonda is surplus to requirements.
Musonda was a bright spark in Chelsea's drab 0-0 draw in the FA Cup at Norwich last weekend.
But the 21-year-old has made just two appearances from the bench in the Premier League this season.
The youngster protested on social media about a lack of opportunities earlier in the campaign.
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But that didn’t stop him from pledging his future to Chelsea following assurances from Antonio Conte.
Musonda scored twice for Chelsea’s Under-21s against Portsmouth in the Checkatrade Trophy this week.
Bournemouth, Watford, Newcastle and West Brom are all keen to boost their attacking options this month, with Musonda on their radar.
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Chelsea have dealt with all four clubs in recent years, but would insist that Musonda is guaranteed playing time wherever he goes.
He played no part as Conte's side played out a goalless draw with Arsenal in the Carabao Cup yesterday.
The Blues host Leicester in the Premier League on Saturday (3pm).