"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.
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.
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.
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.
"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.
