The El Mundo Deportivo newspaper claimed that Florentino Perez, the favorite to become the Spanish club's next president, was considering Laudrup, 44, to take over as Real trainer from Juande Ramos if he won the club's summer elections.
Sovetski Sport said that Perez was a longtime admirer of Laudrup's preference for stylish and elegant football.
Jose Mourinho, Raphael Benitez and Arsene Wenger have also been mentioned as possible candidates to take over from Ramos at Real.
Laudrup played for the club from 1994 to 1996, helping the team to the 1995 La Liga title, and after four seasons managing his hometown club, Brondby, to two Danish cups and a league title, he returned to Spain with Getafe.
In his one season in the Spanish capital he won admirers for Getafe's attacking, attractive football, taking them to the Copa del Rey final and the quarterfinals of the 2008 UEFA Cup, but finishing just 14th in the league.
He took over at Spartak Moscow in September 2008 but was fired late on Wednesday after a 3-0 defeat at home to cross-town rivals Dynamo Moscow in the quarterfinals of the Russian Cup. The club said in a statement that he had been sacked over "unsatisfactory results."
He was the sixth coach in as many years to be dismissed by Spartak. When he took over last September, the side's fans were hopeful that the Dane could replicate the success of another foreign trainer, Zenit St. Petersburg's Dick Advocaat. However, Spartak struggled to find form toward the end of last season, and crashed out of the UEFA Cup at the group stages. Their forward line was particularly weakened by the sale of Roman Pavlyuchenko to Tottenham Hotspur just before Laudrup's arrival
