City Chairman Ray Ranson had spoken to Luton boss and former Sky Blue Mick Harford about the player who has now chosen to move to Norwich City.
Mick Harford told Luton Today: "I spoke to Ray Ranson (Coventry chairman) and he asked me what was going on. "They never came back with an improved offer. It will probably happen in the next 24 hours.
"David Bell has agreed personal terms and had his medical and is in Norwich at the moment preparing to sign. "I think it's an opportunity for him. David stressed to me he didn't want to be at the club."
Norwich City are also reported to be standing by to step in if Michael Mifsud's move to Bristol City breaks down.