Ukraine's football federation has said the two clubs will complete its league season in May and Mutko, returning from a meeting of FIFA's Executive Committee of which he is a member, believes a transfer would then be possible.
"This topic was discussed under an agenda item about sports and political matters at the Exco meeting (and) I have been informed that it is a reality - there are two new clubs in Russia. Yes, they will work within the sporting regulations of the country," he told Russian media on Monday.
"We are interested in friendly relations with Ukraine and are not going to destroy the integrity of its championship. The season ends in May and we will then return to these questions and discuss what the formula would be. This is a matter now for the Russian federation and its Premier League."
FIFA was not available for comment.
Rustam Temirgaliev, the first deputy prime minister of Crimea, also wants the transfer and had a special mention for Tavriya - winner of Ukraine's first Premier League title in 1992.
"With Sports Minister Vitaly Mutko I have discussed the possibility of a participatory transition of Tavriya Simferopol to the Russian Premier League this summer," he said.
"I have also begun talks with a potential sponsor for the club. I hope that, this autumn, we will see Simferopol playing Zenit St. Petersburg, Spartak Moscow and Rubin Kazan."
Nikolai Gostev, president of the Football Federation of Crimea, is also keen but understands the process will take time.
"We would like to become part of the Russian Football Union but it's not so simple. We need to be released by the Football Federation of Ukraine and admitted as a member of the RFU," he told Ukrainian media.
"I talked to the president of the RFU Nikolai Tolstykh and I hope this issue will be resolved on March 27, when UEFA will hold a meeting in Astana."
There have been discussions about expanding the Russian Premier League from 16 to 18 teams in order to accommodate the two clubs from the Crimean peninsula. This would certainly suit the president of FC Sevastopol, Alexander Krasilnikov.
"Our club wants to play at the level we are used to and does not want to go down to the lower divisions. Is the Russian Premier League ready to expand to take us? We will write to the Russian Football Union to discuss these things," he said.
"Of course, we want to know our destiny by the beginning of next season, but the decision will be taken by UEFA and FIFA."
On March 21, Krasilnikov offered his resignation from the executive committee of the Football Federation of Ukraine.
"Please exclude me, Alexander Krasilnikov, from the members of the executive committee of the Football Federation of Ukraine in connection with the entry of Crimea and Sevastopol to the Russian Federation," he wrote.
"As a citizen of Russia, I can not perform the duties of the Executive Committee of the FFU."
In the 16-team Ukraine league FC Sevastopol are in 11th position but Tavriya are 14th with nine points from 19 games. The only two clubs beneath them are Metalurg Zaporizhya (eight points) and Arsenal Kiev, who have no points after going bankrupt.
- Sports & Recreation
- Russian Premier League
- Premier League
- FC Sevastopol
- Football Federation of Ukraine