Rovers face a transitional period now, as they look to assess which players can be retained or released, ahead of a testing campaign in the lower tier.
But Cockayne, 33, is keen to stay and help the Robins succeed in returning to Super League at the first attempt.
“[Hull KR have] been a big part of my life and will continue to be so for next year and as long as they want me in whatever capacity,” Cockayne stated on his personal Facebook page.
“I’m a fairly loyal person when I find true love/friendship and I found it in 2006 with Hull KR and all the people involved.
“Saturday was without a doubt the toughest day I’ve experienced in the colours. As the dust is settling and reality has now kicked in the desire and determination to help lead the charge back to Super League is already burning strong inside me.
“Thank you for all the kind messages and well wishes and of course a few of my ruthless mates who always make you realise that you shouldn’t take life too seriously because we only get one and never know when it can be taken away.
“So as bad as it felt the last few days let’s not forget there are many more people in far worse situations than us around the world, but at the same time let’s remember that awful feeling we had Saturday, and use it as motivation for us to go on and succeed in 2017.”