Laudrup revealed he had been saddened to see the Glasgow giants continue to be plagued by off-field problems since dropping down to the fourth tier of Scottish football.
The legendary winger had hoped the Light Blues would go from strength to strength after they emerged from their financial difficulties two years ago.
However, unhappiness with a succession of directors and executives has steadily escalated as tens of millions of pounds of income has been squandered.
Matters came to a head this summer when many fans decided not to renew their season tickets - until they received assurances over the future of the stadium and training ground.
The bitter stand-off has resulted in vastly reduced numbers of supporters signing up to watch Ally McCoist's side in action at home in the SPFL Championship in the 2014/15 campaign.
The club has now admitted that additional funding will have to be found to meet running costs in the coming season and another share issue will be held for existing shareholders later in the year.
And at the weekend around 3,000 disgruntled fans marched on Ibrox in a rally organised by the Sons of Struth protest group to demand guarantees over the stadium.
Laudrup still takes a keen interest in the fortunes of the Glasgow club, where he spent four years during a glorious spell in the 1990s, from his homeland in Denmark.
He stressed he would like to see senior Rangers officials to do everything in their power to mend their fractured relationship with a sizeable section of their followers.
Because he feels they need to work as one if the 54-times Scottish champions are to become a dominant force again in football in this country AND get back into European competition.
His appeal came as Rangers announced they had set up a nominations committee whose job will be to draw up a shortlist of supporters to be elected to an official fans' board.
He said: "I just hope Rangers supporters can look forward to watching the club playing at the level they deserve to be at in the top flight and in Europe once again soon.
"I hope they will be back where they once were soon. That is what the supporters deserve. They love the club so much. I am keeping my fingers crossed that that is what is going to happen.
"But I know there have been more setbacks along the way. I have read online there are still problems off the park and there are still issues between the club and the supporters.
"I hope that these can be sorted out soon. The club need to have the supporters behind them if they are to get Rangers back to the level they should be playing at in Scotland and in Europe.
"I think whatever concerns the fans have about the club and the direction it is heading in need to be looked at because Rangers need to have them firmly behind them."