"If Russia's bid to host the World Cup wins, the Prime Minister will be ready to fly out to Zurich," the spokesman told local media on Thursday.
The announcement will be made at 1500 GMT.
On Wednesday, Putin had criticised the voting process, saying his country had faced "unscrupulous competition" in the bid to host the World Cup.
Putin, in an apparent blast at British media, said FIFA officials were being smeared and called on other political leaders to follow his example and stay away from FIFA's vote on Thursday to choose the hosts of the 2018 and 2022 World Cups.
"We have unfortunately witnessed a campaign against members of the FIFA executive - filth and compromising material has been poured over them. I see this as unscrupulous competition ahead of the vote," he told ministers in Moscow on Wednesday.
"I would have liked to have gone myself but under these conditions, I have decided to refrain from travelling out of respect for the members of FIFA, the members of the FIFA executive, so that they can make a decision calmly without any pressure from the outside.
"Russia wants and hopes and has the ability, including financial, to host this largest of tournaments. If we are given the chance we will do this in the best possible way."
