Muskwe was one of four first-team players not given a squad number at Luton this season and manager Rob Edwards is keen to finalise his squad for the Hatters’ Premier League campaign in the coming days.
The 24-year-old striker spent last season on loan in League One at Fleetwood, where he scored three league goals in 12 appearances.
Muskwe is entering the final year of his contract at Luton, which has an additional optional year that the club do not plan to trigger, and Championship side Rotherham are keeping tabs on the Zimbabwean.
While selling Muskwe is Luton’s preference, they would also consider a loan move. However, Muskwe is on inflated wages due to Luton’s promotion to the Premier League, so they would likely have to pay a percentage of his salary were he to leave on loan.
Luton have already seen Sonny Bradley and Harry Isted leave on free transfers this summer, sold Carlos Mendes Gomes to Bolton, and sent five players on loan. Midfielder Henri Lansbury retired at the end of last season.
Besides Muskwe, Luton are also willing to sell midfielders Glen Rea, Dion Pereira and former Arsenal man Luke Freeman.