The 20-year-old was plucked from non-league Faversham Town in 2011 and has impressed ever since making the move to Teesside.
Huddersfield and Blackburn have been linked, together with United's North East neighbours Sunderland and Middlesbrough.
"It'll cost you, a lot!" said Cooper when asked about whether there was a price on Baldwin's head.
"I think we've got a lot of players that are attracting attention and playing the way we have done will only intensify that.
"The list of scouts coming to watch our team is getting longer. I think on Saturday in the FA Cup we had 15 scouts watching and a lot of them are from high-end clubs so we know they are watching.
"I've already spoken to a couple of managers regarding players. The thing about football is, if you're not in the top end of football there's not a lot of money.
"It's nice for Jack, he's been outstanding pretty much all of the season and has carried on the form he showed in League 1.
"It's a big shot in the arm for Jack that people are watching. It's lovely as a manager to get that recognition to know the players are doing well.
"You've got to have certain attributes and the way we are playing is attracting clubs.
"I think we have to do what's best for the player and for the club, but if a Premier League club came knocking on the door for Jack Baldwin, I don't think I could turn that dream down, but we'd do it on the right terms.
"As it stands at the moment I'd be surprised if there's people out there willing to open their cheque books."