Now on his 15th Tour, the oldest rider in the field wants to beat Dutch cyclist Joop Zoetemelk's record of 16 appearances by racing through 2008.
Ekimov, nicknamed "Eki," is an Olympic gold and silver medalist and could end his career at the 2008 Beijing Games.
Monday was the first rest day of the three-week Tour. The race resumes Tuesday with a flat stage from Bordeaux to Dax in southwest France.
If Ekimov finishes this year's race, he will have ridden more than 58,000 kilometers in the Tour alone.
Ekimov won gold in the time-trial at the Sydney Olympics in 2000, and silver at Athens 2004, the AP reports.
After it turned out that Deputy Prime Minister Andrei Belousov included the Fonbet betting company in the list of backbone enterprises that can count on state support, everyone started talking about these bookmakers.