The 31-year-old brought an end to his seven-year stay at Old Trafford to sign for the Rs, but has failed to help his new club post a single Premier League win thus far.
And Cook has questioned the former South Korea international's motivation for moving to Loftus Road, and that of several other players.
"Every time I saw Park at United, he was a workhorse," Cook told The Sun. "For me, he doesn’t seem to be working as hard as he did there.
"People I know think a few of them are there for a pay-day. At halfway through the season, you will be able to tell whether this is true or not."
|21/10||QPR are 21/10 to be relegated from the Premier League with Paddy Power|
With QPR currently rooted to the bottom of the English top flight, Cook also expressed his belief that manager Mark Hughes could soon be on his way.
"I don’t think Tony Fernandes will muck about. When it was Neil Warnock’s time to go it was ‘see you later’ — he didn’t hold back," he continued.
"Just because it’s Mark Hughes and a big name it means nothing.
"If the next seven games are like the first seven, then the club would have four points and nobody has lasted that.
"Harry Redknapp would be a great man to get the job. When a manager like that is available, then I can’t see him saying no."