And he is believed to be willing to offer players in exchange to secure the Bairns skipper on a pre-contract for next season.
The Dons boss concedes Hibernian are in a stronger position to finalise a deal for the 24-year-old, while Dundee United are also said to be in the running.
"The next step is to speak to Falkirk to find out if it will be possible to do a deal with them about Barr," explained McGhee.
"We may have to be creative if we are to get anything done that would see Barr brought in this month. But if Falkirk insist on a fee then we will be out of the equation.
"Hibs are in a stronger position than us because they have taken in a fair amount in transfer fees over the last few years.
"We might be better equipped to compete if we sell some of our young talents for bumper fees in the years ahead. For now though, we must live within our means."
Aberdeen 4/6, Draw 13/5, Kilmarnock 9/2