Cooper and Berardi both missed Leeds’ first two pre-season friendlies in Ireland.
However, Monk is optimistic that the pair will both be back fit in the near future.
“Hopefully it’s not too long,” Monk said.
“We’ve had checks so hopefully we’re talking days rather than weeks or months.”
It is not entirely clear how much training Cooper and Berardi were able to participate in during Leeds’ tour of Ireland.
The pair both travelled, but were not able to prove their ability to Monk on the field.
Cooper and Berardi are both likely to be included in Leeds’ first starting line-up of the season if they do make it back fit.
Leeds are on the verge of signing a right-back (YEP), but Berardi appears set to continue as first choice.
Leeds’ Championship campaign gets underway with a match against Queens Park Rangers at Loftus Road.