The National Trust for Scotland has confirmed it is looking at the terms of the lease of the first minister's Edinburgh residence, Bute House.
Bute House is Jack McConnell's official residence
The property is rented to Jack McConnell by the trust. It currently charges a peppercorn amount but is looking for a "fair, commercial rent".
Reports have suggested that similar properties in Edinburgh could fetch about £150,000-a-year.
A NTS spokesman confirmed both parties were close to finalising the new lease.
The Georgian property, in the capital's prestigious Charlotte Square, was designed by Robert Adam in 1792.
It is regularly used by the first minister for hosting colleagues and dignitaries.