Laudrup endorsed, cautiously, for Denmark job
"Michael's success at Swansea does not undermine his chances of being the Danish national coach," Jim Stjerne Hansen, general secretary of the Danish Football Association (DBU), told the local news agency Ritzau.
But Hansen then pointed out that it was still too early to pass judgment on Laudrup's tenure at Swansea, who are ninth in the Premier League at the midway point of the season.
"Michael has gone from being a big success in Swansea, to a doubtful success, to a big success again. Things move so fast in this business, it's not possible to see half a year into the future," he said.
With both men on contracts that are due to expire in 2014, speculation has been rife in the Danish media that Laudrup would take over from the long-serving Olsen.
Widely acknowledged as Denmark's greatest player of all time, Laudrup's name is high up on the list of those that could succeed arguably the country's greatest coach.
Hansen said last year that he had approached him about succeeding Olsen, but then extended Olsen's contract after the Danes qualified for Euro 2012.
Should he be appointed as Olsen's successor when his current contract runs out, Laudrup would be taking over from the man who gave him his first opportunity in management.
Olsen appointed Laudrup as his assistant in the Danish setup in 2000 and together they took Denmark to the knockout stages of the 2002 World Cup before Laudrup left to take over as manager of Copenhagen club Brondby.
And though his glittering career as a player saw him represent the lieks of Juventus, Barcelona and Real Madrid, Laudrup's managerial achievements have been a lot more modest.
Successful stints at Brondby and Spanish La Liga side Getafe were followed by a short sojourn at Spartak Moscow and an unhappy stay at cash-strapped Mallorca in Spain.
But Laudrup got his managerial career back on track when he joined Swansea as a replacement for Brendan Rogers in June 2012.
Swansea were expected to struggle to survive in the Premier League but they have now amassed 25 points under Laudrup and are sitting comfortably in ninth place.
They are one place ahead of Liverpool on goal difference, with ex-Swansea boss Rogers struggling to make his mark at his new club in a marked contrast to Laudrup's success at Swansea.
Throughout his management career Laudrup - who famously missed Denmark's Euro 92 triumph after falling out with coach Richard Moller Nielsen - has remained committed to Olsen's style of free-flowing, attacking football.
And among those recommending him as the next Denmark coach is Olsen himself, who has long held that Laudrup would be a perfect replacement for him.
"He has the qualities and the qualifications, the background as a top player, and he's been a coach for a few years now," Olsen told the Politiken newspaper in 2010.