Valdes had an unsuccessful spell at Manchester United but worked with Pep Guardiola at Barcelona with substantially more success.
Valdes has been released by United having played just the two games for the club. City are on the lookout for another goalkeeper and the Guardian's report states they are looking into the availability of the 34-year-old, who spent the second half of last season on loan at Standard Liege where he made seven appearances.
If such a move does materialise, it is hard to envisage Valdes taking the first choice goalkeeping position off Joe Hart but it is clear that new manager Pep Guardiola wants, at the very least, some competition for the England international.
Guardiola knows Valdes very well given the two had a very successful time together at the Nou Camp from 2008 until Guardiola's departure in 2012, where they won three La Liga titles, two Champions League's and the Copa Del Rey on two occasions.
It does represent a change in approach in terms of trying to recruit a new goalkeeper, with the Daily Telegraph reporting back in March that City were confident of signing current Barcelona goalkeeper Marc Andre Ter-Stegen.
That was at a time when it seems the German was unhappy about the lack of game time he was getting with Barcelona, and it seemed that only a move to a club where he would have been first choice will have taken place.
If Valdes does move to City, it would be interesting to see precisely what Guardiola has in mind, as he would be bringing in a goalkeeper who knows exactly how his approach works.
Would he be expected to be a serious challenger for the number one spot in the side? One would doubt it, but the move would raise one or two eyebrows.