The International Cycling Union (UCI) and the World Anti-Doping Agency (WADA) have appealed against the Spanish Cycling Federation's decision to clear Contador of doping after he tested positive for Clenbuterol during the 2010 Tour de France.
The Court of Arbitration for Sport had set a hearing date of June 6-8 but and had promised to try and issue a verdict before the start of the Tour de France on July 2. However, all parties have now accepted the case requires further time and have yet to set a new date for the hearing.
Riis said Contador has the right to take part in the Tour de France.
"At the moment there's no reason why Alberto can't ride the Tour de France," he said while at the Giro d'Italia.
"It's always been logical to me. He was declared innocent and he's been cleared to race. We've got to respect that right. Nobody talked about it (his right to race) before the Giro d'Italia or the other races he rode, so why is it problem now?"
Respect for the judicial process
Riis agreed that it would have been better for everyone involved, and for the wider good of the sport, if the case had been resolved before the Tour de France. But he called for people to respect the judicial process.
"I think everybody, including Alberto, would have liked the whole thing to be sorted out before the Tour de France. But there's nothing we can do about it. It's a complicated case that needs time to resolve," Riis argued.
"Things haven’t changed in the last few days with the case. We've all got to respect the speed of the judicial process. It's not nice for anybody, for us, or for the Tour de France but things have to be done right for justice to be done."
Riis is convinced the public can understand the reasons for the drawn out legal process.
"I think the public can see the real problem here," Riis claimed, insinuating that the delays in the case were not caused by Contador.
"A lot of the things that have been said and written have only complicate the issue. There's a lot of speculation of how it will all end but we've all got to wait for the outcome of the case."
"I think everyone can also understand the problems that Alberto is facing. If he's really innocent that it's a really difficult situation for him to handle."
Riis is already looking forward to a battle between Contador and Andy Schleck at the Tour de France.
"Alberto is different to Andy Schleck but I'm not interested in comparing them. I just hope we can see a great fight between them at the Tour de France. It'll be great for cycling," he said.