Mr Mundell has remained the sole Tory MP in Scotland after the election
Shadow Scottish Secretary David Mundell has backed the idea of cabinet jobs being given to the Lib Dems as part of any coalition deal with the Tories.
Scotland's only Tory MP said he would "not have an issue" with any specific posts being given to the other party.
Mr Mundell said it was more important to have an arrangement to ensure a period of stable government.
He spoke out after reports suggested a Lib Dem could become Scottish secretary as part of a coalition deal.
Mr Mundell, who represents Dumfriesshire, Clydesdale and Tweeddale, is again the sole Tory MP in Scotland following the election.
The Liberal Democrats have 11 MPs in Scotland.
The Tories, who have 306 seats across the UK, are negotiating with the Lib Dems in a bid to form a new government with an overall majority in the Westminster parliament.
Asked if he would be happy to stand aside and see a Liberal Democrat become Scottish secretary, Mr Mundell told BBC Radio Scotland's Good Morning Scotland programme: "I don't have an issue with any specific Cabinet posts being given to the Liberal Democrats.
"We need to know where we're going and I think that will be clear today, maybe tomorrow, in the sense as to whether an arrangement with the Liberal Democrats is possible, because I think the negotiating teams will be close to hammering out what they could agree."
Mr Mundell said Labour had lost the election, despite doing well in Scotland, and insisted Gordon Brown no longer had the authority to continue as prime minister.
"Therefore it is incumbent on the Conservatives to try to work with the Liberal Democrats and get a deal," he added.
"The stability of our country and getting a government has to be the priority."
However SNP Westminster leader Angus Robertson said a deal between the Tories and the Liberal Democrats was the "worst option for Scotland".
He said: "Scotland didn't vote for that, 85% of us did not vote for the Tories.
"If the Lib Dems want to be the midwives for a Conservative government I think they will rue the day electorally that they did that."
Whatever happens there does need to be a government that can actually take the decisions that need to be taken
The Scottish Nationalists favour a "progressive alliance" involving Labour and the Liberal Democrats, along with themselves and other smaller parties.
Mr Robertson urged the Liberal Democrats to "explore all avenues, not just one avenue".
Meanwhile, Chancellor Alistair Darling said it was natural the Liberal Democrats would go to the Tories because of the arithmetic, but added some would have "reservations about climbing into bed with the Tories".
Labour would talk to the Liberal Democrats if it "doesn't work" with the Conservatives, he said.
But he warned the talks between the Liberal Democrats and Tories cannot "drag on".
He added: "Whatever happens there does need to be a government that can actually take the decisions that need to be taken."