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Unfavoured Musonda has only made two starts for the Blues this season, both of which coming in the Carabao Cup.
Foot Mercato report that Arsenal are now considering moving for the 21-year-old, who is ready for the move.
Musonda turned down a summer loan move away from Stamford Bridge in a bid to battle for a first-team spot.
But as that has not materialised, he is reportedly pushing for pastures new – but could yet remain in London.
Arsene Wenger is not known for splashing the cash in January transfer windows and has hinted he will again avoid spending this time around.
Arsenal fans had been hoping Wenger would go all out to bag Monaco winger Thomas Lemar – after failing to grab his top target in the summer.
The Gunners submitted a £90m bid on deadline day for the France international but they ran out of time to finalise the deal.
Arsenal boss Wenger didn’t buy any new players in the winter window last year with on four permanent additions joining in the past five seasons.
The Frenchman has suggested he is more likely to ditch players in his squad rather than increase his already bulky team.
“No. At the moment I have a big squad,” Wenger said ahead of Thursday clash with Red Star Belgrade. “The problem for me is to keep everyone together until the end of the season.
“Do we go into the transfer market in January? I don’t know yet.”