Valdes has been a free agent since leaving the Catalan giants last summer.
But the 32-year-old has been training with United for three months in order to help him recover from the anterior cruciate ligament injury he suffered in March.
And it appears that United will now sign the Spanish World Cup winner to provide competition for first choice David de Gea.
Valdes came through the youth ranks at Barcelona and spent nearly two decades at the club.
He won six domestic titles, three Champions Leagues and also lifted the Copa del Rey on two occasions. The goalkeeper also won the World Cup with Spain in 2010 and the European Championship two years later.
United manager Louis van Gaal knows Valdes well – he gave the Spaniard his debut during his second spell as Barca boss.
When asked in October whether he would consider signing Valdes if he returned to full fitness, Van Gaal said: “Manchester United has always their eyes open.
Van Gaal’s back-up goalkeeper Anders Lindegaard was linked with a move away from United in the summer and is yet to play a first-team fixture this season.