Thompson is one of seven AFL coaches out of contract at the end of this year, but Cook, who himself knocked back a job offer to be the inaugural CEO at the Gold Coast, said the club was very confident about keeping the man who guided them to the 2007 flag.
While Cook said he would have liked to put the contract issue to bed prior to the season, not doing so wasn't a problem.
And he wouldn't speculate on when it would be done.
"It's like asking how long's a piece of string, really – it could be a month, it could be four months," Cook said.
"We're not intense about it and neither is Mark. He's pretty laid back about it, and so are we.
"We don't think Mark's going anywhere – I'm pretty sure of that, and we expect that he'll sign before the end of the year. It could happen now, or it could happen in four months."
Thompson, who has now coached more games (211) than he played (202), was the man to decide how long the deal would be for, Cook said.
"One or two years, that'll be his call. We're easy whether it's one or two."
He said the club had been able to keep key personnel – on and off the field – in recent years, and he could see no reason why that situation would change.
"Maybe the Gold Coast will put a bit more pressure on us, and Western Sydney will, but I'm very confident that we will keep all the people that we want to keep at this club in the next three years."
