According to the Guardian, Guardiola is considering an offer for Valdez, who is available on a free transfer after leaving the Red Devils this summer.
The 34-year-old made only two first-team appearances due to a fall-out with the former Manchester United manager Louis van Gaal.
Valdes was subsequently loaned out to Belgian club Standard Liege. The goalkeeper joined the club on loan in January and returned in April. Valdez helped Standard beat Club Brugge to win the Belgian Cup in March.
With Barcelona Valdez won La Liga six times and the Champions League three times. A cruciate ligament injury suffered in March 2014 ended his career at the Camp Nou after announcing he was leaving the club in the summer of 2014.