Leeds United are currently in fifth place in the Championship table.
Cooper limped off during Leeds’ FA Cup tie against Cambridge United last Monday with a knee problem.
With Pontus Jansson out with suspension, Leeds’ options are short in defence - with Kyle Bartley the only recognised senior centre-back definitely available for their match against Derby.
And Monk admits that although he is hopeful that Cooper will return, he may be forced to switch Ayling to centre-back.
“He (Luke) can cover that position so that’s obviously a strength but of course you don’t want to try and move players too much out of their position,” Monk said.
“But we are hopeful that Coops will be okay and that we won’t have to move too many but if we do then obviously we will come up with the right way to do it.”
If Ayling does play at centre-back, it means that Lewie Coyle is likely to take his place on the right-hand side of Leeds’ defence.
If Leeds can get past the challenge of Derby it will be a major statement of intent, ahead of this weekend’s Championship matches.
Leeds will could up to third place in the table with a victory, and they would be within four points of automatic promotion chasing Newcastle United.