FC travel to Wigan on Friday evening to battle for a place in the Super League Grand Final at Old Trafford next Saturday.
KR, in contrast, are playing the Million Pound game at home against Salford, with the loser being relegated to the Championship.
“I hope FC win two more and win the Grand Final,” Cooke told Love Rugby League.
“I hope KR win at the weekend and secure Super League survival.
“And I mean that with the utmost respect to Salford.
Cooke believes that rugby league in Hull would benefit from both teams doing well, and he anticipates that Rovers will enjoy a much better campaign in 2017, as long as they stay up.
“The state of things at the minute is good, obviously for Hull FC,” he added.
“If Hull KR can stay up and Neil Hudgell sticks to his word regarding spending some money, then they can certainly be a force and be back within the top eight echelon next year.
“It’s all to play for this weekend, for both clubs.
“If you’re asking me which result would I prefer this weekend, then I would prefer Hull KR to stay up, for the reasons I mentioned earlier, for the sake of the sport and city.
“But I certainly hope Hull FC win the next two.”