Forming the backdrop to the match are the tensions over the alleged presence of Chechen rebels on Georgian territory, and Russian threats to cross the border and take military action against them.
Earlier this week, when the two presidents met in the Moldovan capital, Chisinau, and agreed on joint border patrols, Mr Putin opened the talks with a reference to the forthcoming game.
"Soon, you know, the soccer match will take place, Eduard Amvrosiyevich," Putin was quoted as saying by the Kommersant newspaper.
The match takes place in the Georgian capital, Tbilisi, and Mr Shevardnadze is expected to attend.
Given the present climate, however, some Russian politicians have suggested the venue should be changed.
"It is impossible to allow the match to take place in the capital of Georgia," said ultranationalist Vladimir Zhirinovsky, on Ekho Moskvy radio.
"It needs to be moved to neutral territory."
Mr Zhirinovski even predicted Russia would win 5 - 0.
Low expectations
Georgians do not expect the result to be that bad for their national team, but expectations are low.
Although the squad has a number of skilful players there is little team spirit.
The heydays of the Georgian football - when Dynamo Tbilisi was one of the most successful Soviet clubs - are over.
Georgia slumped to a 4 - 1 defeat to Switzerland in its first qualifying game last month, whereas Russia beat Ireland 4 - 2.
Georgia's star player, Kakha Kaladze, has been quoted by a Russian newspaper as saying: "Let's leave the politics to the politicians, I am a soccer player."
He himself has been a victim of the lawlessness of Georgia's Pankisi Gorge, which Chechen rebels have used to shelter from Russian forces in Chechnya.
His brother is still missing after being kidnapped in Tbilisi last year. He is thought to be being held in the gorge.
After the kidnapping Mr Kaladze said he would never play for Georgia again, but later relented.