Ms Dugdale had been widely tipped to stand for the position of Scottish Labour leader after Mr Murphy stepped down at the weekend, when he narrowly survived a vote of no confidence at the party’s ruling body.
Her remarks came after Scottish Labour held its first group meeting at Holyrood today since leader Mr Murphy announced his intention to resign next month.
Ms Dugdale, when asked after the meeting if she would stand for the position, 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.”
The Scotsman revealed yesterday that Labour MSP Ken Macintosh has already started canvassing among MSPs for a potential leadership bid, which he is expected to formally announce later.
Mr Macintosh said any leadership election for Scottish Labour should be conducted through a one member one vote ballot along similar lines to the UK contest to succeed Ed Miliband as party leader.
He 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.”
Mr Murphy, who lost his East Renfrewshire seat in the SNP rout on 7 May, attended today’s Scottish Labour meeting at Holyrood,
He said: “I will watch with great interest and keep out of the leadership process.”