Sky Sports News have contacted ASO for comment.
He was later banned for two years for doping and stripped of his 2010 Tour win.
Team Sky have already appealed the decision, per the report, with a final outcome expected on Wednesday - just three days before the race starts in Briancon on Saturday.
The Brit has been continued to compete despite the ongoing doping case against him and won the Giro D'Italia in May.
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Five-time Tour victor Bernard Hinault, who worked for the Tour organisation for many years, last month called for the peloton to strike if the British rider lines up at the start of this year's event next Saturday.
Sky, ASO and the French Olympic Committee will each choose an arbiter to decide whether Froome should be allowed to start the Tour. He has faced criticism from some fellow and former riders, suggesting he should step aside from competing while the case remains unresolved.
UCI president David Lappartient reacted to the story on the sidelines of the French national championships.
Froome and Team Sky have denied any wrongdoing. We didn't know anything, as always, even if it's hard to believe.
Froome's victory at the Giro - after earlier wins in the Vuelta and Tour - meant he became only the seventh man to complete a Grand Tour hat-trick.
Groupama-FDJ boss Marc Madiot has also praised the Tour de France organisers for the decision.