The reports, which are supported by news coming out of Denmark, say the Dane's representatives have been contacted by Celtic.
However, they also claim that Laudrup has been offered the manager's job at Granada.
It throws another curve ball into the intriguing game of finding the successor to Neil Lennon.
Laudrup and his assistant, former Hoops hero, Morten Wieghorst, would be an intriguing Danish double act at Parkhead.
They have been out of work since parting company with Swansea in February after Laudrup fell out with his employers over time spent away from the club.
The 49-year-old reached a settlement with the Premier League side at the end of last week and is now actively seeking a fresh challenge.
The former Lazio, Juventus, Barcelona, Real Madrid and Ajax star has previously managed Getafe and Majorca in Spain, as well as Brondby in his homeland and Spartak Moscow in Russia's top flight.
Durng his 18 months in Wales, he led Swansea to a League Cup final win, their first major trophy in their 100-year history, but cracks were already beginning to show in his relationship with his employers.
And after a bad run of results at the start of this year, Laudrup, along with Wieghorst, was sacked.
Wieghorst was a popular player at Parkhead and won a lot of admirers for the way he bravely battled back after contracting Guillane-Barre Syndrome in 2000.
He went on to manage FC Nordsjaelland in his homeland before taking over the Danish Under-21 side, then accepting the offer to join Laudrup at Swansea last year.
Wieghorst admits he is honoured to be linked to a return to Paradise and said: "It's a massive club and I would be interested if I got a call."
Meanwhile, David Marshall has tipped his old boss at Cardiff, Malky Mackay, to be a success if he is given the green light to take over the Parkhead hot seat.
The Scotland goalkeeper - who has met Celtic stars Scott Brown, Charlie Mulgrew and Leigh Griffiths for tomorrow's friendly at Craven Cottage against Nigeria - can fully understand why Mackay is one of the men at the head of the field.
He said: "It would be a good job for Malky.
"His stock is high with what he did for us at Cardiff.
"As an ex-Celtic player who has done well taking us to the Premier League, I think he must be up there in the running for it.
"It's a completely different job at Celtic, but he will know that, and that' something he has in his favour.
"He was at Celtic from a young age, so knows how big the club is, how big the job is, and how important it is.
He went on: "I was surprised when I heard Lenny had gone because I thought he was settled there.
"The next job he picks will be big for him, and I hope he can get a Premiership club."