The Blues have had approaches from clubs in the United Kingdom and overseas for Musonda, but are happy to take their time before sanctioning any move away, Goal understands.
The 21-year-old was left disappointed with his previous loan spell at Celtic and the Premier League club are keen to avoid a repeat scenario of his Scottish experience, which saw an 18-month deal conclude prematurely in May after just six appearances.
Blues boss Maurizio Sarri has included Musonda in his pre-season group ahead of the new campaign and the Belgium Under-21 international is understood to be enjoying the chance to show his skillset to the new manager.
The midfielder has also been the subject of interest over a permanent move away from west London, but he remains highly regarded at Stamford Bridge, with his contract running until 2022.
However, the youngster faces stiff competition for a place in the first team squad and is looking for game time to build on the handful of senior appearances he made for Chelsea and Celtic last season.
Sarri's switch to 4-3-3 in the 1-0 friendly win over Perth Glory offered Musonda an opportunity to impress in midfield as he replaced Ross Barkley after 77 minutes and he will be keen for more chances.
Musonda's desire for more competitive action is also driven by his international ambitions with Belgium as he looks to break into the senior squad following the World Cup.
The Brussels native is on the radar of Red Devils boss Roberto Martinez, who is hopeful that the Blues youngster can take his development to the next level.