Despite his unhappiness at Serie A giants AC Milan - where he had been on loan from Fiorentina - he had still performed with all of his usual professionalism.
And the Dane played for the San Siro club on no fewer than seven occasions during their triumphant Champions League campaign the previous season.
So it was no surprise that many of the top clubs on the continent started to eye the former Brondby, Bayer Uerdingen and Bayern Munich midfielder covetously.
The chances of Rangers, despite their dominance of Scottish football around that time, landing the highly-prized player appeared slender.
Yet Laudrup decided that joining the Ibrox club was the right move for him - after spending just a few minutes in the company of manager Walter Smith.
The winger, a free spirit on the pitch, had never felt entirely comfortable during his time in the ultra-defensive Italian top flight and felt he needed to revive his ailing career.
Listening to Smith speak in a private room at Cameron House Hotel at Loch Lomond, it soon became apparent to the player that he would be able to rediscover his love of the beautiful game in Scotland.
"Walter told me exactly why he wanted to bring me to Rangers," said Laudrup.
"He told me what his ideas were and where he wanted to play me.
"He told me that he wanted to give me the freedom to play wherever I wanted to play on the park. I immediately bonded very well with Walter.
"As he talked, I started to think that joining Rangers would be a good move for me. You have to consider that over in Italy I was playing in a very restricted role on the right side of midfield.
"So when I heard Walter say that I was going to be given freedom to express myself I was sold. I decided there and then that it was the right move for me."
Laudrup had fulfilled a long-held ambition when he signed for Fiorentina after helping Denmark to win the European Championship in Sweden two years earlier.
However, the old adage "be careful what you wish for" proved to be accurate; he was thoroughly miserable both professionally on the park and personally off of it.
"I had two difficult years in Italy," he said. "It had always been a dream of mine to play there. I used to go over there to visit my brother Michael when he played for Lazio and Juventus and going there was attractive to me.
"In those days, to play in Italy was considered to be the ultimate for any professional footballer. Serie A was the best league in the world.
"I won the European Championship with Denmark in 1992 and got my move to Fiorentina.
"I wouldn't go so far as to say it was a nightmare. In terms of gaining experience, it was definitely beneficial. But what I learned from that time was that I was restricted on the pitch and the style of football did not suit me.
"People in the south of Italy can also be very emotional. Sometimes football is like life or death to them.
"It was difficult at times for both myself and for my family to deal with that."
HE ADDED: "I have always been somebody who wanted to have a life outside the game. I wanted to be a normal person off the pitch. That was very, very difficult in Italy.
"Fiorentina were relegated to Serie B in my season there. It was a major blow. We had a fantastic team in my opinion. But we had two or three new coaches in my time there and there was a lot of upheaval and unrest.
"I ended up going out on loan to AC Milan. I played for them in their run to the Champions League final, but I still just didn't enjoy my football. Towards the end of the season I hadn't been playing as much as I would have liked.
"A lot of clubs were interested in signing me. But only on loan. I was only interested in talking to a club who wanted to sign me permanently and where I could play for two or three years. That is when the move to Rangers came about."
When news of the Scottish champions' interest in him filtered back to Laudrup, he agreed to jet over to Glasgow to hear what they had to say.
"I didn't know much about Rangers at the time," he admitted. "I had seen them playing in Europe and knew some of their players.
"But I wasn't aware of just how big a club they were. I flew in and was greeted at Glasgow Airport by John Greig. He took me to Ibrox and showed me around the stadium. From there, we went in his car to Cameron House.
"I met Walter and pretty much decided there and then that it was the right move for me. After that, everything was sorted out very quickly. A deal was agreed and signed within two or three days. I was on my way to Scotland."
The rest is history.