Valdes sustained a serious knee injury in March after announcing that the 2013/14 season would be his last with Barca after 12 years in the first team.
Following his medical in the principality on Wednesday, Monaco's vice-president Vadim Vasyliev said: "He is injured and will not come here."
However, the ex-Barcelona keeper's agent Ginés Carvajal maintains that his client will complete the planned move.
He is quoted as saying by Spanish paper AS: "We have a four-year contract signed with Monaco and it will be upheld."
If Monaco cannot be persuaded, the 32-year-old will remain a free agent and must convince a new club of his fitness to play.
Valdes made 535 appearances for Barcelona, winning six La Liga titles and three Champions Leagues. He was part of Spain's triumphant 2010 World Cup and Euro 2012 squads and has won 20 caps for his country.
Barcelona have replaced Valdes with the highly-rated German Marc-Andre Ter Stegen and Chile's World Cup goalkeeper Claudio Bravo.
- Sports & Recreation