The 26-year-old has been strongly linked with a number of Premier League teams including Chelsea, United and Tottenham.
But Chelsea signed Nemanja Matic earlier this transfer window, and are not expected to do any more business after agreeing a deal for Kurt Zouma today.
Likewise, United manager David Moyes has said he does not expect any more additions to his Old Trafford squad before tonight's deadline.
At one stage Guarin was heavily tipped to join Chelsea, but the Stamford Bridge side seem to have dropped their interest.
The Gazprom-backed outfit have the funds, but like Galatasaray, they do not play in a prestigious domestic competition.
And Guarin, with the World Cup on the horizon, wants to keep his profile high to ensure himself of the best possible chance to play a starring role this summer.
Another fact to consider - Zenit will be in no hurry in their pursuit of Guarin as the Russian transfer window does not close until the end of February.