The Tractor Boys increased their bid to £3.75 million, but the Bluebirds are believed to want to at least match the £4 million fee they paid Sunderland for the 26-year-old a year ago.
Chopra played for manager Roy Keane at Sunderland, and is said to fancy the chance of a move to Portman Road.
He is on holiday but will have talks with Davey Jones as soon as he returns home.
