But his love of the Ibrox club, where he feels he produced the best football of his life, still burns as strongly now as it ever did.
And the Dane has revealed the trauma the Glasgow giants have endured in the last few years has been heart-rending.
He was at Rangers at a time when some of the biggest names in the European game, himself included, were signed in multi-million pound deals.
Walter Smith's star-studded side dominated domestically as a result and completed - thanks to a rare headed goal from Laudrup against Dundee United - nine-in-a-row in 1997.
So seeing the once-great institution suffer financial meltdown and then get dumped into the Third Division alongside part-time minnows shocked him.
"When the news first broke about all of the off-field problems that Rangers were having I was pretty devastated," he said.
"I still try to keep in touch with what is happening at Rangers by going online and I couldn't believe the stories that I was reading at the time.
"For any Rangers supporter or any former Rangers player, it was very hard to bear when the club was relegated to the fourth tier of Scottish football. For me, it was like losing one of my nearest ones.
"It was really hard to watch what happened to the club from over here in Denmark."
Despite his anger, disbelief and sadness at the fate that befell his former club, Laudrup always believed that Rangers would, in due course, recover.
For he believed that in manager Ally McCoist they had exactly the right man to lead them through the leagues and back into the top flight of Scottish football.
The winger struck up an excellent understanding on the pitch with the prolific striker during the four years he spent plying his trade in this country and they enjoyed a good relationship off it.
In that halcyon spell, he witnessed McCoist's affection for the club he had grown up supporting as a boy and also his strength of character.
So Laudrup is not surprised the record Rangers goalscorer, aided by his old team-mate Ian Durrant, has successfully steered the club to back-to-back promotions in the last two seasons.
And he remains optimistic, despite the continuing unrest at Ibrox, that the Gers will complete "The Journey" by beating Hearts and Hibs to the SPFL Championship title in the 2014/15 campaign.
"Knowing that Coisty was there and knowing that Durranty was there alongside him on the coaching staff gave me hope that Rangers could come back," he said.
"There was great camaraderie in the dressing room when I played at Rangers. We had some real characters in the team and Coisty and Durranty were two of them.
"We were professional about the game and did everything that we possibly could to play well and be successful. But off the park we had big fun.
"It was how football should be. At some of the other clubs I played at in my career you would train in the morning and then you wouldn't see your team-mates until the next morning.
"At Rangers it was all about having a great time on and off the park."
Laudrup added: "Coisty and Durranty are guys who love the club, who live, sleep, eat and breathe Rangers.
"I knew that with them both involved there was a good chance that Rangers would survive and would get back to where they belong.
"And that is exactly what has happened and what is continuing to happen.
"They have a great chance to get back into the top flight this season. It would be great to see if they do."
Joining their Old Firm rivals Celtic in the SPFL Premiership next year would be a major milestone for Rangers as they strive to become a major force in Scottish football again.
But Laudrup, who is now a respected television pundit on Champions League nights over in his homeland, feels they should aim higher than that.
He reckons that getting back into Europe's premier club competition and taking on the continent's elite again should be an objective for the Govan club.
Performances in that tournament often left much to be desired when the midfielder played for Rangers, but he reckons that is the level that a club of such a size and stature belong at.
He said: "I would obviously like to see Rangers back in the top division and competing for the title and the League Cup and the Scottish Cup. That is the level they should be at.
"There is a long way to go, but they should also be thinking about playing in the Europa League and playing in the Champions League once again as well.
"European nights at Ibrox were always fantastic occasions.
"It is a level the supporters are used to seeing their team play at and I am sure they will do so again in the future."