The Finnish Football Association declined to comment but said it would be holding a news conference on Monday. Local broadcaster MTV reported that assistant coach Markku Kanerva would be replacing the 64-year-old Swede.
The team have not won a match since Backe took charge in January. Finland are fifth in 2018 World Cup Group I qualifying with one point from four games.
Backe has previously coached FC Copenhagen and New York Red Bulls. He has also worked among the backroom staff for Mexico and at Manchester City.
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Finland, who are ranked 93rd in the world, have never qualified for the finals of the World Cup or European Championship.
(Reporting by Jussi Rosendahl; Editing by Tony Jimenez)
