The Championship club are considering whether to make a move before the loan window closes.
Having not featured for the Canaries since January, and having made just one Premier League appearance all season, it appears that Alex Neil will not stand in the 28-year-old's way if a suitable bid comes in for the forward as the Mail reports that it was the striker that turned down a loan move to an unnamed club in January.
However, the Blues may have some competition if they hope to land the former Rangers man. The Daily Mail previously reported that Championship rivals Leeds United were keen on the striker, and with teams set to enter the home straight of the season, managers may be willing to take a punt on Lafferty in the hope that he is able to bag the goals that either get them promoted or keep them up.
It would arguably be a gamble if Gary Rowett decided to sign the Northern Ireland international. While he has been a goal machine for his country in recent times - scoring seven goals during Euro 2016 qualifiers to help Michael O'Neill's side stun everyone to reach the finals this summer - his club form in recent seasons is much less impressive.
Last season, in 34 appearances for both Norwich and Turkish side Rizespor, Lafferty scored just three goals so may not be the answer if Rowett was hoping to sign a striker that may be able to help them claw back the six point gap that currently separates them from the division's top six.