Cardiff enjoyed a spell in the Premier League in the 2013-14 season when they were relegated under Ole Gunnar Solkjaer.
Neil Warnock has led them to the Premier League again having secured automatic promotion along with Wolves this season.
Wales Online reports that Snodgrass is top of Warnock’s wishlist in the summer, and the deal could be arranged.
The 30-year-old has two years left on his West Ham deal, but doubts remain whether he will play for the Hammers again.
He played 43 matches for Aston Villa last season, and enjoyed a fruitful loan spell, managing eight goals and 13 assists.
The winger, disregarded by owner David Sullivan, may not feature in the plans of new manager Manuel Pellegrini.
Snodgrass has previously worked with Warnock in 2012, during their time together at Leeds, before he completed a move to Norwich City.
The report suggests that the Welsh club could look at a loan deal for the player who is rated at £12 million by the Irons.