A road trip for two could cost supporters more than £2,000 and would involve a minimum of 30 hours driving time, the motoring organisation said.
Such a trip could also be dangerous as there are high accident rates on Russian roads, the AA said.
Those attempting the drive from Manchester would be faced with a 2,000 mile journey to reach Moscow, while Chelsea fans would have to travel 1,800 miles.
The AA is advising those who choose not to, or who cannot, fly to take boat or train trips to Moscow for the May 21 match.
AA president Edmund King said: "It looks as if most flights to Moscow or to other cities in the region are already fully booked, so some fans will seriously consider clubbing together to drive to Moscow. However, they shouldn't underestimate just how much planning and preparation would be required, and the costs too. There would be a lot of paperwork to sort out including extending your car insurance to cover Russia and Belarus, obtaining visas, and getting breakdown cover for that region is difficult. You'll also be driving on very unfamiliar roads with different motoring regulations, as well as the difficulty of the language barrier."
One hundred motorists are killed and another 800 injured each day in Russia while road accident rates are twice as high in Belarus and Poland than in Western Europe.
Digg
Delicious
Spurl
Newsvine
Furl
Reddit
Yahoo!