The Blues are not happy with the lack of game time the 21-year-old has accrued since joining the Scottish champions in the January transfer window.
Musonda, who is currently absent with a shoulder problem and receiving treatment at Chelsea's Cobham Training Centre, has started only three times for the Glasgow giants and has made a total of eight appearances.
Celtic won a competitive race for the Belgian in January and there is no shortage of interest from Europe's big leagues in the winger.
Musonda's mother, Angela, posted on Twitter that her son was "back for good", suggesting that the loan deal was effectively over, though Celtic boss Brendan Rodgers has since denied that is the case.
"Charly hurt his shoulder in the week when he was away," said Rodgers. "He has gone back to Chelsea to get treatment on that. So like I say, he may or may not feature between now and the end of the season.
About yesterday.. living in the moment👊🏽🌟— Angela Musonda (@angiemusonda) May 6, 2018
We got back to the UK safely and found a good surprise.. our baby son Musonda is back for good. Am happy😃
Summer holidays are almost here.
Zambia 🇿🇲 we had fun and we will be back soon❤️ pic.twitter.com/v7ObqWFFzO
“But he is obviously a Chelsea player so they want to look at him to make sure he is okay.”
The Northern Irishman is a former youth coach at Chelsea, but there is a chance that his light use of the attacker may affect his chances of securing more youngsters from the Stamford Bridge club.
Chelsea renewed Musonda's contract until 2022 in December and he scored his first goal for his parent club this season against Nottingham Forest.