The Leeds signing has been discussing the 18-year-old playmaker.
Indeed, the 26-year-old signed for Leeds on loan from Sunderland on Thursday afternoon and praised teenager Cook when he was asked if he sees himself playing alongside the playmaker.
Ultimately, however, Bridcutt understands the final call will always lie with the manager.
Bridcutt told BBC Radio Leeds: "Obviously I've seen Cook play for a couple of seasons, he's been a great player and is going to be a top player.
"I've made a name for myself as more of a defensive midfielder. It's the manager's decision [whether I play]."
Boss Steve Evans now has a variety of options within the Leeds midfield but that won't take the emphasis off whoever the Scot does decide to start.
The midfield battle will be key against Queens Park Rangers this weekend and Leeds' creative talents need to find a way of getting their forwards more involved.
Obviously, the wide men and Chris Wood need to up their efforts themselves - but it will be up the likes of Cook and co to pick them out and create chances they simply can't miss. Bridcutt's presence as a holding midfielder could free United's more creative players up to do that.