A season-long deal had been agreed between the two clubs, but the Potters are now fighting to salvage the situation and secure Popov a work permit.
The 27-year-old, who came to Stoke boss Tony Pulis' attention when the sides met in the Europa League last season, has played 42 times for Macedonia, but the country is ranked only 102nd in the world.
Popov told the Stoke Sentinel: "I am disappointed because I came here and I saw that Stoke is so good for me. That is why I wanted to stay so much, but I cannot change anything.
"This was my dream from starting to play football, to play in England. I played against Stoke City for Dynamo Kiev and I saw it was a good club. I saw also the stadium is nice and every game it is full with 28,000 people.
"You play against big teams here. I would say football in England is the best in the world.
"Everything was ready for me to sign, but then they say there is a problem with the work permit. It is so difficult with the Macedonia national team because we are ranked 102. Before we were in 60th place and that was good, but now it is bad.
"The problem is not the clubs, the problem is the rules here in England. It is crazy. I cannot believe it."
While Popov has seemingly resigned himself to returning to Kiev, a Stoke spokesman described the move as "hitting difficulties" rather than having completely collapsed.
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