Tosic, 22, is on World Cup duty with the Serbia squad, but will finalise the permanent move away from Old Trafford after his country's campaign.
The winger struggled to fulfil his potential at United but after growing tired of a lack of first team football, he was loaned to Bundesliga side Cologne where he enjoyed good form, scoring 5 goals.
Cologne were in talks with the Red Devils about a permanent deal, and Tosic had also expressed a wish to rejoin the club, but CSKA have reportedly made an £8million bid.
The Russian club, who reached the quarter-finals of the Champions League last season, see Tosic as an ideal replacement for fellow Serbian Milos Krasic who is on his way out of the club.
However, Cologne director Michael Meier concedes revealed they are unable to compete with the offer for the Manchester United winger.
Speaking to Express, he said: "We made him an offer to stay.
"But the sums of money put before him make it hard for any German club to compete."
Meier remains grateful to Tosic for helping his club avoid relegation last season with his inspired performances.
He added: "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.
"But, in the end, there are only winners in the deal."
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