A solution could be found in Monaco next week when all parties would gather on the sidelines of the Champions League group-stage draw. That draw could include Zenit St. Petersburg, owned by Russian industrial giant Gazprom - a top-tier Champions league sponsor - and which counted Mutko among former presidents.
Uefa has publicly expressed hope that the Russian and Ukrainian federations would find a compromise.
''If they would come up with a joint proposal that would be a very nice signal,'' Uefa general secretary Gianni Infantino said this month, without suggesting which side might concede ground.
''Football sometimes makes miracles.''
Meanwhile, the question of Russia's World Cup stadiums was on the agenda in Sochi, according to Fifa.
Blatter suggested ''a possible reduction in the number of venues for the 2018 Fifa World Cup as well as matters linked to the capacity of the arenas''.
Mutko responded Tuesday, defending the plan agreed with Fifa two years ago.
''The conception, under which 12 stadiums in 11 cities will host World Cup matches, is not being changed,'' Mutko said, according to the ITAR-Tass agency.