Deputy Scottish Labour leader Kezia Dugdale is expected to announce if she will stand for the party leadership by the end of the week.
Scottish Labour held its first group meeting at Holyrood today since leader Jim Murphy announced his intention to resign next month at a press conference on Saturday.
Ken Macintosh, a veteran MSP and the party’s social justice spokesman, has also expressed an interest in standing for the leadership.
Ms Dugdale, who was elected to Holyrood in 2011, said: “I am going to make a decision in the next couple of days.”
Asked if she will make an announcement by the end of the week, she said: “That’s the plan.”
Mr Macintosh said: “There’s a lot to go before we actually agree the leadership process and there will be no formal declarations until that point.
“I think that it is fair to say that I have certainly indicated to some of my colleagues already that I am interested in putting my name forward.
“But at this stage we need to agree a leadership process itself.
“I think it is fundamental that we move to Omov (one member one vote).
“I am very much in favour of the union link.
“But the Omov system, if we have got it for the national party we need it for the local party.”
When asked if it needs to be sorted out quickly, he said: “Yes I do. Well, we have got a month. We know what the process is going to be.
“But I also hope the leadership itself is also a quick process because we have got an election in a year’s time.
“But there will be no formal declarations until we have that process in place.”
Mr Murphy, who remains in charge until next month, said: “I will watch with great interest and keep out of the leadership process.”
Mr Murphy announced his intention to resign on Saturday, after just five monthsat the helm, despite a narrow endorsement by the party’s Scottish executive in avote of no confidence following Labour’s near wipe-out in Scotland in theGeneral Election.
The result sparked the prompt resignation from Scottish Labour’s shadow cabinet of Alex Rowley, Gordon Brown’s former constituency agent who was elected to Holyrood in the January 2014 by-election, and Neil Findlay, who stood against Mr Murphy last year having failed to convince Mr Brown to stand.
Several unions also called on Mr Murphy to resign.
Mr Murphy will spend the next month devising a package of reforms to hand down to his successor, warning that if the party then goes on to block his “urgent” measures it will do so “at its peril”.
The reforms include ditching the electoral college system under which all previous leaders have been elected, which requires the endorsement of at least two of the three colleges comprising parliamentarians, party members and trade unions.
Mr Murphy launched a parting shot at “disruptive” Unite boss Len McCluskey on Saturday.
He said he had to resign despite the executive endorsement because the “small minority” who tried to block his election in December “won’t accept the vote of the executive and will continue to divide the party if I remain”.
He said OMOV is vital to ensure his successor can “lead with an authority that can never be challenged”.
“The Labour Party’s problem is not the link with the trade unions, or even the relationship with Unite members, far from it,” he said.
“It is the destructive behaviour of one high-profile trade unionist.”
He added: “The leader of the Scottish Labour Party doesn’t serve at the grace of Len McCluskey and the next leader of the UK Labour Party should not be picked by Len McCluskey.”