"Gary is back on the road to fitness but with his injury he's in for a long, hard summer of reflection about his time here so far," Cooper told the Sunday Sun.
"If your heart and soul aren't 100 per cent in it it's difficult to move forward. You want players who want to be here, but Gary's said nothing to me to suggest he doesn't want to be here.
"He's been brilliant for us, he had a great season. He works his socks off and he gives us balance and energy down the right wing.
"I just hope the summer will give him time to think about things and hopefully he'll realise that Middlesbrough's the best place for him to be.
"The same goes for George. He has been fantastic for us, I've got a lot of time for him and I hope he stays."