The Spanish goalkeeper is a free agent after deciding not to renew his contract with La Liga giants Barcelona.
Valdes had been widely expected to join up with big-spending Monaco ahead of the new campaign.
However, Monaco president Vadim Vasilyev revealed earlier on Thursday that the 32-year-old would not make the switch to Stade Louis II because he had failed to recover sufficiently from a serious knee injury sustained against Celta Vigo in March.
Valdes' agent, Gines Carvajal, has subsequently refuted those claims and stated Monaco will have to honour a prior agreement that was reached between the two parties.
"We have signed a four-year contract with Monaco and we will enforce (it)," Carvajal is quoted by Marca.
Valdes spent 12 years at Camp Nou, where he won six La Liga titles and three UEFA Champions League medals.