"The decision has been taken," the Austria Press Agency quoted Michael Häupl as saying. He added that a formal decision will be taken on Tuesday by the party's directorate.
Kern, 50, is widely credited with turning around Austria's creaking national rail company. Experts say that as an outsider he is well placed to heal rifts within the Social Democrats (SPÖ).
Faymann, 56, quit on Monday two weeks after a historic defeat in the first round of an election for the largely ceremonial post of president at the hands of the far-right Freedom Party (FPÖ).
The Social Democrats and centre-right People's Party (ÖVP) have dominated Austrian politics since 1945 but support has been falling for years, and they only just managed to scratch together a majority at the last general election in 2013.
Like elsewhere in Europe, they have been bleeding support to fringe groups, in particular to the populist FPÖ after almost a million migrants passed
through Austria last year.
The FPÖ under Heinz-Christian Strache is leading opinion polls with more than 30 percent, compared to the low 20s for the SPÖ and ÖVP, ahead of the next election scheduled for 2018.
Faymann took a harder line on migrants in recent months, but this failed to boost his support and alienated many in the SPÖ, particularly those in the left wing of the party.
The final straw was the first round of the presidential election on April 24 when the FPÖ'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 FPÖ, 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 SPÖ when he was young, moving up the ranks before moving to an energy firm in 1997 and joining its management board in 2007. Three years later he switched to national railways company ÖBB.
There, he is widely credited with achieving a turnaround and with successfully managing the transport of immense numbers of migrants transiting through in 2015.
"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 ÖBB boss to really stand by his workers," Roman Hebenstreit of the ÖBB works council said Friday.
"He is a natural-born striker... Under him ÖBB's motto was 'Now things are moving'. Following this wouldn't do the government any harm," Hebenstreit told public radio.
But whether Kern can heal rifts within the SPÖ remains to be seen. His positions on key policy areas are vague, although he is thought to lean more to the right on economic issues.
His biggest headache will be to decide whether to ditch the SPÖ's 30-year-old taboo on cooperating with the FPÖ, dating back to when the late, controversial Jörg Haider became leader of the right-wing party.
There have been growing calls within the centre-left to tie up with the FPÖ, at least at local level. Others though, including the SPÖ's youth wing, vigorously oppose this.
Kern also needs to revitalise the SPÖ's deadlocked coalition with the ÖVP and agree structural reforms to get Austria's economy, faltering of late, moving again.
ÖVP head Reinhold Mitterlehner praised Kern's "management qualities" in an interview published Friday, but said that this was "the much-quoted last chance" for the coalition.
"The task before him is Herculean," political analyst Thomas Hofer told AFP, saying he expected Kern will be a "pragmatist" with regard to the far-right and in other areas.