The Bluebirds offered the midfielder a fresh two-year deal yesterday.
Gers boss Ally McCoist is keen to sign Cowie, who is out of contract this summer.
The 31-year-old played a major part in helping the Welsh side reach the Premier League, but then lost his place last season.
Cardiff boss Ole Gunnar Solskjaer holds the key and if Cowie gets an assurance that he will get his chance then he is likely to remain.
Rangers have been on the former Ross County player’s trail for weeks. McCoist spoke to the player and then asked chief executive Graham Wallace to make an offer, but it’s understood that has not yet happened.
Blackburn Rovers are also keen on Cowie.Â
McCoist, who is hoping to add another two players, has already signed strikers Kris Boyd and Kenny Miller, and defender Darren McGregor from St Mirren.