The defensive duo are both out of contract and new boss Ian Murray says he hasn’t had too much in the way of contact with the players as both have made it clear they want to move on.
Musonda was deployed more often than not as a utility player having joined Rovers in 2020, but losing Tumilty will prove more of a blow.
The 25-year-old has barely missed a minute in his right back berth during two seasons at Stark’s Park and was winner of the Fife Free Press Star Check Award in 2020/21.
Murray said: “Tumilty has made it no secret that he wants to leave the club so there's not been too much dialogue there. Musonda as well is looking to leave.
“I know Frankie did really well but sometimes you have to change things around to try and get better and take a chance.”
Also out of contract is midfielder Brad Spencer, but Murray says negotiations there are more promising.
“The situation with Brad is slightly different. We've had a good dialogue with him,” he says.
“That's ongoing at the moment. He's a player that I like and I know he did very well last season.
“He had a couple of small injuries around October time and possibly coincided with a little dip in form for the team.
“Brad's done great and we're keeping in contact with him.
“He's on holiday at the moment, it's difficult at this time of year to get face to face with players but over the next seven to 10 days we'll have some news on Brad one way or the other.”