The Tory leader is being urged to avoid making David Mundell the next Scottish Secretary, the Sunday Herald understands.

In a sign of growing unease about his ability, Mundell was not invited to a dinner with Cameron in Scotland last week, despite being the only Tory MP north of the border.

One alternative being considered is to ennoble an MSP in order to serve as Scottish Secretary from the House of Lords.

The Conservative Party is anxious about the implications for Scotland of a Tory win at the next General Election.

There are fears that Salmond, who privately savours the prospect of a Cameron victory, would use it as a battering ram to demand a referendum on independence.

It had been assumed that Mundell, a Dumfriesshire MP since 2005 and an ally of the UK Conservative leader, would be certain to become the party’s first Scottish Secretary since Michael Forsyth.

However, the Sunday Herald can reveal that several senior Tories regard Mundell as a political lightweight who is simply not up to the job of keeping the combative First Minister in check.

Mundell’s critics want a more substantial figure for the post, but are worried about the lack of options, especially as the party would be lucky to return six Scottish MPs at the General Election.

It is understood that while Mundell is still favourite for the post, senior Tories at Westminster would welcome an alternative. Cameron could look to another Scottish MP from next year’s intake, although this is thought unlikely as the Tory leader is closer to Mundell than he is to any of the prospective MPs north of the border.

Another idea being discussed internally is to give a senior MSP a peerage, and then the keys to the Scotland Office.

One source said: “Mundell is not Cabinet-level material, but getting rid of him presents the problem of a viable alternative.

“There are good people, but few will be in the Scottish group at Westminster.”

Another source said there was a “live debate” inside the party about who will be the next Scottish Secretary.

It is understood that the “David problem”, as it has been described, was discussed at the Tory conference in Manchester.

Another Tory insider insisted that it was “significant” that Mundell was not asked to a private dinner at the Milngavie home of Sir Jack Harvie, the Tories’ key Scottish fundraiser, on Friday.

Cameron attended alongside Lord Strathclyde, the Tory leader in the Lords, and around a dozen Tory sympathisers in the business world.

Scottish Tory leader Annabel Goldie was also not invited, despite living just a half-hour’s drive away in Bishopton.

Mundell, who is nicknamed “Fluffy” by colleagues, is unpopular with many Tory MSPs for writing unflattering “report cards” about them for Cameron.

One MSP said: “David has his limitations.”

Dumfries Labour MP Russell Brown said: “Clearly, even the Tories don’t think that David Mundell cuts the mustard.

“The fact that they are planning such a drastic measure indicates how little support the Tories have in many parts of Scotland.

“And for Annabel Goldie to be excluded from meeting her own donors is embarrassing.”

An SNP spokesperson said: “Instead of fretting about who should be Scottish Secretary, any future government should scrap this inefficient £7.2 million propaganda post and invest the money in frontline Scottish services instead.”

A Scottish Tory spokesman said of the debate surrounding the dissatisfaction or otherwise with Mundell: “No comment.”

Asked why Goldie and Mundell had not been invited to the Harvie dinner, he added: “You are looking for mischief where none exists.”