A spokesman for the Britannic Lift Company, which has its premises in Riverview Buildings, Bradford Road, confirmed the business was looking to relocate.
He said no decision had been taken on where the new base would be, but that it would be somewhere “within the West Yorkshire area”.
In 2003 the business, which then employed more than 100 staff, was bought by the German conglomerate ThyssenKrupp.
No one was available for comment at Thyssen-Krupp’s UK head office this week, but it is believed the local Britannic Lift office could close and its staff could be moved to a regional office in Leeds. It would also cease to trade under the Britannic name.