The striker, who joined the League One outfit on loan until the end of the season on Friday, returned to the Liberty Stadium on Monday in mysterious circumstances, it has been reported in the South Wales Evening Post.
Donnelly had been expected to feature for Steven Pressley's side in Tuesday night's game at Bristol City, but that now looks unlikely.
If the 21-year-old returns to Swansea on a full-time basis, he will be ineligible to play for the club's under-21 side because he is officially a Coventry player until the end of the season.
"Both clubs are working on a solution to the situation but he'll certainly not be available for tomorrow night," he said.
"It's a disappointment because we obviously worked hard to get in a couple of strikers ahead of the window closing but that's football and that's what we're faced with."
