Ayala, on loan from Liverpool, sits out a one-game ban after reaching five bookings and Cooper feels he is ready to step up from the reserves to make his third league appearance for his hometown club at Barnsley this weekend.
The 19-year-old said: "It would be nice to think I might have a chance for Saturday, but that will be up to the manager.
"I'm here to be counted and if I do get the chance I'll go in and do the best I can for the team.
"Whoever I play for, I put in 100%, but when it comes to Hull City I will always try to go that little bit further with it being my hometown club.
"I just want to be in the first team again and hopefully that will come in the near future."