The 26-year-old former-Arsenal midfielder has been linked with a return to the Premier League, and both Arsenal and United need reinforcements in the summer.
And Eto'o, who left Barcelona for Inter Milan in 2009, believes Song must leave the Nou Camp too if he wants to improve as a player.
"Song has to leave Barca," Eto'o told beIN Sports. "At his age, he must play and he could be in the starting XI at any big club."
Song said earlier this month that if he were to leave Barca this summer, it would be to return to the Premier League.
He played his best football in England for Arsenal, before eventually moving to Spain in the summer of 2012.
United boss David Moyes could get as much as £200m to spend this summer, and central midfield is a real area of concern for the manager.
Song, a defensive midfielder, could be an asset to Moyes at Old Trafford but a return to the Emirates Stadium and the opportunity to link up with Arsene Wenger again may hold the greater appeal.
Song did not feature as Barcelona beat Real Madrid 4-3 in El Clasico on Sunday night, with an inspired Leo Messi scoring three goals and providing an assist for Andres Iniesta.