Hayes, 29, has scored six goals in 22 matches for the Scottish Premiership side this season, including one in the Europa League.
He won the 2010 Scottish First Division title with Inverness and then the 2014 Scottish League Cup with Aberdeen.
Cardiff have already signed utility player Greg Halford from Championship rivals Rotherham and striker Ibrahim Meite from non-league Harrow Borough.
Now they are trying to add Hayes, who has two caps for the Republic, as manager Neil Warnock looks to revamp his squad in the January transfer window.
Cardiff City are targeting Aberdeen's Republic of Ireland winger Jonny Hayes.