MK Dons manager Paul Ince is expected to be named as the man to succeed Mark Hughes but Laudrup appears to be in the running after holding talks with Rovers chairman John Williams in Zurich.
The 44-year-old, who has also played for Juventus, Lazio, Real Madrid and Ajax, resigned as manager of Spanish club Getafe last month.
In the running: Getafe's Danish coach Michael Laudrup
'In 20 years of working in football I have not come across a chairman as
impressive as John Williams," Laudrup's agent Bayram Tutumlu told the Daily Telegraph.
'He spoke to Michael about the history of the club and of the potential for the future.
'He (Laudrup) was not sure about Blackburn before the meeting, but he is now thinking very seriously about this club."
Williams, after announcing on Tuesday he hoped to be able to name the new manager by the end of the week, seems to have reassessed their position.
'Nobody has been offered the job," he said.
'We are continuing the process and all candidates are aware of the position. We will appoint someone as soon as we are ready."
Yesterday the League Managers' Association said they would have no objections were Ince to be named Blackburn manager, despite his lack of a UEFA Pro Licence.
The Premier League could block his appointment due to his current lack of formal coaching qualifications and Ince would need special dispensation to take the role, similar to that given to former England team-mate Gareth Southgate.
Southgate got the green light to manage Middlesbrough two years ago without being licensed.
The decision to allow Southgate to continue as Boro boss upset the LMA but current chief executive Richard Bevan, who was appointed in September, insists he will not lobby against Ince's appointment.
He told Sky Sports News: 'It's a Premier League rule. The Premier League has made exceptions to it in the past and that's up to them.
'From our perspective, if any manager wants help to get qualifications, either football related or non-football related, we are here to help.
'We would support Paul Ince if he got the Blackburn job.'
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