Indurain and his Banesto team could not be reached for comment.
The paper says Indurain has said his best days are behind him.
Indurain, 32, won the Olympic time-trial at Atlanta in August when the sport's top professionals competed in the Games for the first time.
His contract with Banesto forces him to ride in the Tour of Spain, which starts on Saturday, for the first time in four years.
Banesto had already contacted Spain's 1995 world champion Abraham Olano, who rides for the Italian team Mapei, to replace Indurain, AS reported.
Indurain's manager Francis Lafargue said he would not compete for another season just for the money.
"Miguel is a honest man. His engine is as powerful as ever and he is only 32-years-old," Lafargue said.
"But if he feels he can no longer be his former self, he won't do one more season just for the money."
A Banesto spokesman said it was too soon to comment on Indurain's future.
"We are focusing on the Tour of Spain and when the moment comes to renew the contract we will see," he said.
Indurain's contract expires in December.
Indurain, 32, whose contract expires in December, failed to record a sixth successive win in the Tour this year but won gold in the Atlanta Olympics time trial.
``Miguel Indurain is determined to give up cycling this winter,'' As said. ``According to sources close to the Banesto team, Indurain has already shared his decision with close friends.
``Although they are trying to convince him against it, the announcement could be made public in a few days.''
A Banesto spokesman said it was too soon to comment on Indurain's future but his manager Francis Lafargue said he would not compete for another season just for the money.
``Miguel is a honest man. His engine is as powerful as ever and he is only 32 years old,'' Lafargue told the French Sud-Ouest newspaper. ``But if he feels he can no longer be his former self, he won't do one more season just for the money.''
The Banesto spokesman said: ``We are focusing on the Tour of Spain and when the moment comes to renew the contract we will see.''
Last month Indurain said he was not keen to race in the three-week Tour starting in Valencia on Saturday.
``I didn't particularly want to do it but the team decides,'' he said. ``Physically I am well but mentally I'm not.''
The two men have appealed the sentence and will be allowed to continue competing until a second verdict is handed down.
Both tested positive during the Spring European spring competition -- Durand in April and Laurent in early May, when he came second in the "Dunkirk Four Days".
Durand and Laurent have been stripped of their placings in the race in which they tested positive and were each fined 2000 Swiss francs (1600 dollars).
The Frenchmen are considered time-trial specialists, with the former holding the yellow jersey in the early stages of the 1995 Tour de France and both competing in the 1996 Tour.
Durand, 29, won the French road racing championship in 1993 and 1994, while the 30-year old Laurent has previously represented France in international competition.
Their cases bear similiarities to fellow countrymen Phillipe Gaumont and Laurent Desbiens, who were suspended for six months on July 16 after being found guilty of taking the same banned substance.
In that instance, the cyclists revealed that they been taking Nandrolene under prescription. The doctor who authorised the drugs has since had his medical licence revoked.
The French Cycling Federation has refused to comment on the affair.
Meanwhile, in Italy, top Italian cyclists Fabiano Fontanelli and Franco Ballerini have both been banned after failing drugs tests.
Fontanelli is out for six months after high levels of testosterone were found in a sample he gave after finishing fifth at the Amstel Gold Race on April 27.
Ballerini, who won the Paris-Roubaix Cycling Classic in 1995, is banned for 20 days after testing positive for the stimulant ephedrine after winning the Wallon Grand Prix race on May 15.
The FFC refused to reveal what the riders had taken or when their appeal committee would meet to discuss the case. A spokeswoman only confirmed the ban and the appeal.
It is the policy of French cycling authorities not to disclose doping cases or even bans and riders have been known to be out of action for weeks for so-called injuries when actually suspended for drug taking.
The final 34 kilometre stage went to upcoming Australian mountainbiker Cadel Evans, who blitzed the rest of the field to finish more than a minute ahead of nearest rival, Frenchman Thomas Dietsch.
Brentjens won his second Tour after taking the lead in the first stage.
He was victorious in the inaugural event in 1995, and is the current world mountainbike champion.
In the women's event, Norwegian Gunn-Rita Dahle, finished first in the 26.5 kilometre final stage, completing a whitewash of her opponents to win the overall Tour.