The 32-year-old chose not to renew his deal at Barcelona following a 12-year stint between the posts for the Catalan giants.
With Valdes out of contract this summer, Monaco were reportedly keen on recruiting the Spain international for the upcoming Ligue 1 season.
But after Valdes suffered a serious knee injury in Barcelona's league win against Celta Vigo in March, the club have decided against bringing the shot-stopper to France because of doubts over his fitness.
Monaco vice-president and sports director, Vadim Vasilyev, told a press conference on Thursday: "Victor Valdes is injured and he won't join us."
Valdes travelled to France this week to undergo a medical with the Principality club but failed the fitness tests on Wednesday.
The 32-year-old remains a free agent and will now have to convince a new club that he will be fit enough to play next term.
Valdes – who missed out on Spain’s World Cup campaign in Brazil with the anterior cruciate ligament damage in his knee – has won six La Liga titles and three Champions Leagues trophies with Barcelona.
The Catalan club have replaced Valdes and outgoing keeper Jose Manuel Pinto with 31-year-old Chilean goalkeeper Claudio Bravo from Real Sociedad and 22-year-old Marc-Andre ter Stegen from Borussia Monchengladbach.