Cologne have been chasing the player, but they have revealed that they cannot match the Russian side’s offer for the Serb.
The 22 year old is currently on World Cup duty, but a deal looks set to be done after the competition is over.
It’s a blow for Cologne who had the player on loan for the second half of last season where he impressed. Tosic himself was known to want to join Cologne, but they can’t match the £8 million offered by CSKA.
"We made him an offer to stay," said Cologne director Michael Meier.
"But the sums of money put before him make it hard for any German club to compete."
Meier added in Express: "But, in the end, there are only winners in the deal.
"We stayed in the league thanks to Tosic, Zoran was able to show his form and is at the World Cup and Manchester United can achieve their asking price."