The French club are in the market for midfielders this summer and are hoping to add some much-needed experience to their squad.
And 29-year-old Song, currently at Russian club Rubin Kazan, fits the bill for them, according to France Football.
Song has started just 12 of mid-table Rubin's 30 league games so far this term and has been linked with a move away this summer.
And the key to any move to Marseille could be their sporting director Andoni Zubizaretta, who was influential in signing Song for Barcelona from Arsenal in 2012.