Simmonds featured for Killie, who face City on Saturday at Rugby Park, against QPR on Tuesday night and could be interested in a loan north of the border as opportunities at the Ricoh Arena appear very limited.
Simmonds was the second top scorer for City Reserves last season and scored against Nuneaton Town a week ago.
He has been allowed to look for another club by Chris Coleman,despite having a year left on his contract and was on loan at Gillingham at the end of last season.
Said Jim Jeffries to his club's website: "I spoke with Steve Kean and he helped us out. "Coventry are thinking of letting him go out on loan as they feel it would benefit him.
"We gave Donovan 45 minutes against QPR to see what he was like and he's certainly got pace to burn. "We'll let him train with us and we'll see how he does. There is a possibility he may turn out against Coventry on Saturday."