Murphy the Merlin was taking part in Tuesday’s 3pm falconry display at the museum in Leeds Dock when he disappeared from sight.
Merlins are the UK’s smallest bird of prey, with a relatively long, square-cut tail and broad-based pointed wings, shorter than those of other falcon.
Chris Johnson, of SMJ Falconry, said: “Towards the end of the demonstration he went to set down which sometimes he does, then he went out of sight.
“It’s quite important to be able to try to find him tonight.”
The transmitter attached to one his legs has failed, meaning the team are having to resort to more old-fashioned methods in tracking him down.
A number of sightings have been reported today, but Murphy is yet to be caught by his handlers.
Mr Johnson said: “There was a sighting at Granary Wharf near the station. That was this morning at about 9.30am-10.30am.”
Anyone who spots Murphy is asked to call Mr Johnson on 07534 649047.