"The decision has been taken," the Austria Press Agency quoted Michael Haeupl as saying. He added that a formal decision will be taken on Tuesday by the party's directorate.
Faymann, 56, quit on Monday two weeks after a humiliating defeat in the first round of an election for the largely ceremonial post of president at the hands of the far-right Freedom Party (FPOe).
Mirroring similar developments across Europe, the SPOe and its centre-right coalition partner the People's Party (OeVP) have been bleeding support to fringe groups, especially the FPOe.
Faymann took a harder line on migrants in recent months, but this failed to boost his support and alienated many in the SPOe, particularly those in the left wing of the party.
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The final straw was the first round of the presidential election on April 24 when the FPOe's Norbert Hofer scored 35 percent and the main parties' candidates won a dismal 11 percent each.
Hofer, 45, portrayed as a friendly face of the FPOe, will take on Alexander van der Bellen, 72, the professorial former head of the Greens, in a runoff on May 22.
Snappy dresser Kern, 50, grew up in a working class district of Vienna as the son of an electrician and a secretary.
He joined the SPOe when he was young, moving up the ranks before moving to an energy firm in 1997 that he became boss of in 2007. Three years later he switched to national railways company OeBB.
"This is not the time for normal service," the father-of-four said in September at the height of the crisis.
"Kern is someone who got things going... He was the first OeBB boss to really stand by his workers," Roman Hebenstreit of the OeBB works council said Friday.
"He is a natural-born striker... Under him OeBB's motto was 'Now things are moving'. Following this wouldn't do the government any harm," Hebenstreit told public radio.