McMenamin made 25 appearances for Livingston, of the Scottish Premier League (SPL), last season.
There has been no official word from the club as yet, but the news is being reported on a football website, with the 24-year-old striker quoted as saying: "Scottish football is going backwards and there's no money in the game up here."
The forward scored twice in 14 starts last term, and has been on the books of Newcastle United.
He would be Peters' fifth summer signing, and his first striking capture.
Meanwhile, rumours in the West Midlands are linking Luke Rodgers with a move to Walsall. Rodgers rejected a new contract at the Meadow in his search for football at a higher level.