"The problem is if one of our keepers goes down, we would need Mark on the bench," Lawrence explained to the Western Mail.
"There is the option of recalling players if they go out on loan, but I'm not certain you can do that in the first month. In any case, that would be no good for Swansea because they wanted Mark for the rest of the season."
Flynn needs cover as regular stopper Roger Freestone is nursing a back injury
"I made an enquiry about Mark joining us, but basically I've received a refusal from Cardiff," said Flynn.
"A while ago they said they would help us as much as they could. But it doesn't appear to be happening - and that's disappointing."
Flynn will continue his search.