Leonid Fedun, who owns Spartak Moscow soccer club, said: "I am acting as a private individual in this case, and as a fan of the Russian national team."
Fedun has offered to give cars to goalkeeper Stipe Pletikosa, a Spartak player, as well as three outfield players.
A Croatian victory against England, coupled with a Russian win in Andorra, would see Russia leapfrog England in Group E and claim a Euro 2008 place. Wednesday's matches are the last in the group.
Croatia have already secured their qualification for the European Championships.
Offering such incentives is not expressly forbidden under UEFA rules, and is widely believed to be common practice in many European leagues, including the Russian Premier League, where it is known as 'stimulyatsiya' or 'stimulation'.
An English fan took a similar step before Russia's fixture in Israel on Saturday - a game that Israel had to win to keep England's Euro 2008 hopes alive. Fred Done, the founder of the U.K. bookmaker Betfred, offered to give a $100,000 Mercedes car to the scorer of the winning Israeli goal.
However Omer Golan, who became an England national hero by scoring in injury time to hand Israel all three points and deny Russia the chance to move into second place, was forbidden under Israeli FA rules from claiming the car.
While Fedun's promise may not be the only attempt by a Russian businessman to offer an incentive to the Croatians, it is so far the only one to be officially announced.