A number of Labour powerbrokers believe shadow international development secretary Jim Murphy has the best chance of taking on the SNP in 2016.
Lamont was elected Scottish Labour leader in 2011. But party insiders say she does not see herself in the role long-term and could step aside within a year.
Relations between Lamont and her deputy, Anas Sarwar, have also dipped, after she seized control of Labour's referendum campaign from him.
Asked recently whether Lamont would be Labour's candidate for First Minister in 2016, Sarwar said: "Johann Lamont is leader of the Scottish Labour Party."
The post-Lamont jockeying has already begun and several Labour sources, speaking on condition of anonymity, want Murphy to be her successor.
Murphy, MP for East Renfrewshire, was demoted by Ed Miliband in last year's shadow cabinet reshuffle and is believed to have been frozen out by his team. The 46-year-old is not thought to savour another five years in opposition if the Tories win the next general election.
With more or full powers expected to come to Holyrood the Scottish leader's job is a more attractive prospect than it was for MPs at the start of devolution.
One senior source said the "jungle drums are beating" for Murphy. "There are many people in the Labour Party and the wider movement who want to see Jim Murphy throw his hat into the ring for Scottish leader, as he's popular in the party and beyond it. If a vacancy was to arise in the not too distant future he is the candidate who could reach beyond the party base and get us back in the game. He has star quality."
Another insider said: "There has been some pressure on him to do it. People know he gets under Salmond's skin and he commands a huge amount of loyalty. He's a first-class politician."
But a key obstacle for Murphy is securing a Holyrood seat. The Labour selections for target seats are underway and it is not believed the MP would relish being a List member, so he would have to rely on a constituency MSP retiring.
Lamont's failure to introduce one-member-one-vote for the Scottish leadership contest presents a headache in the form of a 30-year-old electoral college. It gives one-third of votes to trade unions and affiliated organisations, which would play against ultra-Blairite Murphy.
He was shadow defence secretary before assuming his role in Ed Miliband's team. He is a leading figure in Better Together and has embarked on a tour of Scottish towns to campaign for a No vote.
Admirers include top Labour donor Willie Haughey, party fixer Frank Roy MP and Ken Macintosh MSP.
SNP MSP Kenneth Gibson said: "It is no surprise that senior Labour figures are deserting Johann Lamont - under her leadership Scottish Labour has abandoned its principles with her Cuts Commission seeking to undo all the progress made since devolution by scrapping key social policies like free prescriptions, free personal care and fee-free university tuition."
Murphy did not respond to a request for comment.