Ince is understood to have travelled to Cardiff to open talks with manager Malkay Mackay, but is yet to commit to the club and is thought to be waiting for another offer to come in.
An agreement was reached with Blackpool for the player over a week ago, but it is understood Ince is holding out for a bid from the likes of Tottenham and Liverpool before completing the signing, having been strongly linked with both clubs previously.
Mackay has made Ince his number one transfer target this summer and is hoping to have done enough to convince the England Under-21 international that his future lies at the Welsh club.
Liverpool did their best to reach an agreement with Blackpool for their former player last January, while Tottenham have failed to follow up their reported interest with an official bid.
Everton have also failed to follow up their interest, while Capital One Cup winners Swansea have also been credited with an interest in the player.
Ince has asked for more time to consider his next step, but is understood to favour a move to one of the league’s established sides despite Mackay’s efforts to convince him he would be the focal point of the Bluebirds midfield going into the new season.