The goalkeeper's contract at Barcelona ran out at the end of June, and the Spain international was expected to join Monaco on a free transfer.
However, a knee injury suffered in a league fixture against Celta Vigo on March 26 required surgery, and it appears the 32-year-old has not recovered sufficiently for Monaco's liking.
"Victor Valdes is injured and will not come," said president Vadim Vasilyev at a press conference to present ne head coach Leonardo Jardim on Thursday.
"Danijel Subasic has all the qualities to be the goalkeeper for the season.
"It has been a very good season and the coach believes in him."
Vasilyev also heaped praise on James Rodriguez, who has proved to be one of the stars of the FIFA World Cup, scoring five goals as Colombia reached the quarter-finals, where they will meet hosts Brazil.
"We had reason to go for James Rodriguez even if his transfer was criticised last year," he said.
"We look forward to working with him next season."
Former Sporting coach Jardim, meanwhile, was excited at the prospect of getting to grips with the players as Monaco look to go one better than the second-place finish they achieved in Ligue 1 last season, behind Paris Saint-Germain.
"I am very pleased to be here today," he said. "The players received my speech very well and the methods I want to implement.
"I have my own personality. My line of work is to train exactly as we will play. We are working to build a competitive team with leaders to meet our objectives."
