Leeds are among a number of clubs thought to have the 29-year-old on their radar, with promoted Sheffield Wednesday also reported to be interested.
But Varney has his sights set on a move to Elland Road where he is keen to work under manager Neil Warnock.
He told the Yorkshire Evening Post: "The other clubs that have been mentioned are still Championship clubs. But they are not clubs of the size of Leeds.
"Neil's got a great record in the Championship and it's something I want to be a part of.
"With coming to Leeds, I can also still get home to see my little child in Leicester and it would be perfect. I'm looking forward to a move to Leeds."
Portsmouth boss Michael Appleton confirmed last week that Varney is in talks with the Whites over a move.
Varney only joined Pompey from Derby last summer and has two years remaining on his deal at Fratton Park, but the cash-strapped club are keen to offload players as they prepare for life in League One following relegation.