The government should use its stake in Bank of Ireland to force it to hand over its building on College Green for use as offices for the proposed new Dublin mayor, according to Fine Gael frontbench spokes­man Leo Varadkar.

In a letter to BoI chief executive Richie Boucher last May, Varadkar noted that the College Green property "formerly accommodated the Irish House of Commons and House of Lords".

"It seems to me that Grattan's parliament would make an excellent home for the new Dublin Regional Authority and the mayoral offices," he wrote. "I wonder if Bank of Ireland would give any consideration to transferring ownership of the buildings to the state in lieu of one of the payments owed to the state under the terms of the bank levy, or the coupon on the monies given to the bank for the purposes of recapitalisation."

However, Varadkar's proposal was rejected by Boucher, who said it could not be considered "at the present time".

In his letter of reply last month, he said the bank had acquired the building shortly after the Act of Union and had used it both as a "working branch and an administrative office building in the period since then".

"The branch has very extensive footfall and a large customer and business customer base," he wrote. "Adjacent to and an intrinsic part of the complex is our main cash centre for the receipt of and distribution of cash to our Dublin branches. The presence of the cash centre is particularly sensitive from a security point of view and makes us cautious about access to the building."

He said the bank was "very much aware" of the historic nature of the building and provides guided tours of the House of Lords. It also makes the House of Lords available for public and private events, he wrote.

"Given this background of the working branch, the overall use of the building, in particular the security aspects, I hope you will understand that we cannot consider disposing of this building in the manner proposed at the present time."

However, Varadkar questioned why the bank needs such a historic building when it has numerous branches around the city.

"If the government decides it wants the building, it should just look for it from Bank of Ireland, which is going to have to pay hundreds of millions of euro to the state in the coming years," he told the Sunday Tribune. "It should seriously look at the possibility of getting some land assets off the banks we have bailed out."