The Scottish champions failed in a bid to sign Motherwell’s Trevor Carson but could return with an improved offer after seeing a reported £200,000 proposal thrown out.
The 29-year-old has impressed since joining Motherwell on a three-year contract in the summer following a £10,000 move from Hartlepool.
Celtic are on the lookout for a keeper after Brendan Rodgers revealed Craig Gordon would be out for 12 weeks with a knee injury, while Musonda will provide some creativity in the absence of Leigh Griffiths, who will be missing for four weeks with a calf problem.
Rodgers claimed Celtic had beaten 24 clubs across Europe to sign Belgium Under-21 international Musonda and the playmaker sensed Glasgow was the right place to continue his career.
Musonda told Celtic TV: “It’s simple for me - Celtic is a massive club. It’s a club with many fans, an unbelievable passion, and the culture is more than a club. Those were the most important things, and I wanted to go somewhere where I would enjoy my football, and I know the manager as well. I am very happy to be here.
“It’s a massive club and I am really looking forward to it. I was quite close to coming last summer but it didn’t happen.
“I spoke again with the manager a couple of weeks ago and I said I had a feeling that this is where I want to come and play my football. I am very lucky to be here and I am very happy to be here.”