The 21-year-old has caught the attention of Premier League sides, while Real Betis are one of many overseas clubs open to bringing him in for the rest of the season.
Although Chelsea moved to extend his contract until 2022 in December, Musonda has made just two Premier League appearances from the bench this season.
He does, however, still have many admirers at Betis, as he impressed during his spell there in 2016.
He has also featured for Chelsea's Under-23s in their journey to the quarter final of the Checkatrade Trophy, where they are competing against League One and League Two sides.
Musonda was pivotal in edging them beyond Portsmouth on Tuesday as he scored both of their goals in the 2-1 win, with his second coming in the 95th minute from a 30 yard free-kick.
Meanwhile, Kenedy is also garnering interest in his services on loan, but he won't be allowed to leave unless the club sign another left sided player.
Newcastle United had a deal agreed in principle for the Brazilian over the summer but it fell through as Chelsea failed to sign another wing-back.
Juventus's Alex Sandro remains the club's main focus but negotiations have so far been unsuccessful.