Russia have not hosted a World Cup or European Championship before but the Champions League final was held in Moscow this year.
Mutko is hoping they can draw on their successful bid to host the Winter Olympics in Sochi in 2014 to aid them in the process.
"We want to organise a sporting event of the highest level," Mutko added. "Nevertheless, we have to take a very close look at all the possibilities.
"We have to have 12 host towns ready and have available at least a dozen stadiums with 40,000 seats for the tournament.