Leeds United have been attempting to sign Lafferty for much of the season so far, but they could now be set to miss out.
The Whites have struggled to agree a deal with Norwich throughout the transfer window so far.
Leeds want to sign Lafferty on loan, but Norwich are more keen for him to leave on a permanent basis.
Bristol City are now hopeful that they can have more success at tying up a deal with the Canaries, as they look to strengthen their squad.
The Robins are battling against relegation in the Championship, and are currently manageress, but they still feel that Lafferty would make a good addition.
The Northern Ireland international is understood to be desperate to play regular first team football, and his chances of doing so at Carrow Road look slim, with Steven Naismith set to arrive from Everton in the near future.