The 24-year-old midfielder, who has also been recently linked with Serie A side Lazio, admitted this week that had it not been for a failed attempt to obtain a work permit, he could be plying his trade with the Premier League leaders.
Red Devils boss Sir Alex Ferguson spoke to Mamaev directly, and told the Russian not to worry about his lack of international caps, that was holding up his prospective Old Trafford switch.
"I was in shock, it was such a dream transfer," he told the Russian media. "The deal was around 80 per cent complete, but with my limited number of caps for Russia, I couldn't get a work permit.
"Sir Alex Ferguson said he would try and solve it, but the contact never came again."
The Russian connection with the Blues is obvious, with billionaire owner Roman Abramovich seeming to have more and more control over transfer activity at the club, particularly under the interim management of Rafa Benitez.
Mamaev's arrival might be regarded as a bit left-field by Chelsea supporters, given his relative obscurity, and the fact he has only been capped twice by his country, with the midfielder's last appearance for Russia coming in 2011.
After impressing for the U21s, scoring four goals in 14 appearances, Mamaev was tipped for a bright future, but has seen his career stagnate in Moscow, and so could be open to a move in the summer as he bids to put himself back in contention for an international call-up.