It was reported last Monday that the Premier League newcomers had made a substantial offer for the England Under-21 international winger, and Sky sources understand the bid they have tabled is worth £8million.
Liverpool also now have a 48-hour window to formally express their interest in the player as part of the deal that took him to Blackpool from Anfield in 2011.
Speaking from Blackpool's pre-season training camp in Portugal on Sunday, the Seasiders manager has admitted his son has a big decision to make but is hopeful that he might choose to remain in the Championship for another season.
"Cardiff have come in massively for Thomas and the chairman has accepted their offer," confirmed Ince senior. "I'm not sure what the offer is as I've been away.
"It's a case of when he comes back, we'll sit down and see what we want to do.
"He loves it here and has told me he's in no rush to leave the club.
"I think it's 50/50 at the moment. It's a tricky one for me - ideally you want your son to be playing in the Premier League, but you also want him to be playing for you.
"I wouldn't put my hat on it that he'll be playing in the Premier League this year."
Thomas Ince, who was named the Football League's Young Player of the Year in March, scored 18 goals in 44 Championship appearances last season.