The Whites have no intention of offloading the Scotland international, having seen him net three times in the opening weeks of the new season.
Middlesbrough, though, have been chasing McCormack for much of the summer and have refused to concede defeat in their pursuit of the 27-year-old.
Leeds have no need to sell, with a contract in place which is due to run until 2015, and Varney hopes they can see out the summer window with McCormack still on the books at Elland Road.
He said in the Yorkshire Evening Post: "It's completely up to Ross, but we're all desperate for him to stay.
"It would be to the massive detriment to the team if he leaves now.
"I'm sure the gaffer's desperate for him to stay too. We all are because he's a great part of our team.
"With the start we've had it would be a huge disappointment to lose him now. Hopefully September comes quick, we keep this squad and get a couple of additions. We've started really well."