Valdes, 32, continues to work his way back from a serious knee injury, having left Barcelona at the end of last season after spending his whole career at the Catalan club.
“I confirm that we’ve been in contact and had negotiations with him and his entourage, but he is injured and won’t sign for Monaco,” said the club’s vice-president, Vadim Vasilyev.
Valdes, who has been capped 20 times by Spain, tore the anterior cruciate ligament in his right knee in March and underwent surgery which ruled him out of the rest of the season as well as the World Cup.
“Today, we are counting on (first-choice goalkeeper) Danijel Subasic who had a very good first season,” added Vasilyev, who also said the club would wait until the end of the World Cup before making a decision over the future of Argentine international Sergio Romero.
Romero, who played second fiddle to Subasic but is his country’s first-choice keeper at the finals in Brazil, spent last season at Monaco on loan from Italian side Sampdoria and has said he would like to extend his stay at the Stade Louis II.
Monaco on Thursday also handed one-year extensions to central defenders Eric Abidal and Ricardo Carvalho, whose contracts had both been set to expire.
Abidal, 34, was given the captaincy last season by former boss Claudio Ranieri, who has since been replaced by Portuguese Leonardo Jardim, and made 26 appearances in Ligue 1 but endured a difficult second half of the campaign and lost his place to Aymen Abdennour.
Carvalho, 36, was an almost ever-present for the club last term, missing just one league match, as Monaco finished second, behind champions Paris Saint-Germain, with a club-record 80 points.