The team behind the proposed 28-storey Kite Tower on the site of the Leeds International Pool still believes the skyscraper could get built in the city.
Designed by Make Architects, the 91m mixed-use development lost out to a scheme by HBG Properties and housebuilder Barratt, following a design competition in January.
But both Ken Shuttleworth's practice and backer Urban Catalyst remain confident that the tower could yet be constructed.
There are even rumours that the landmark scheme, developed with Leeds-based practice Carey Jones, may make a grand reappearance on the original site.
Nikolaj Dockree, a development executive at Urban Catalyst, said: 'When we lost out we were, I like to think, a very close second and we had a fantastic scheme.
'[The Kite] would be a great statement for the city, and we would like to do something, but it is very much down to the council.
'The current developer has had nearly three months to put in a proposal and now there are only four weeks left. If it doesn't, we will be pushing hard to put something on the site or on another site in Leeds, ' Dockree added.
Sean Affleck, a partner at Make, is also optimistic that the project could still get the green light.
'Urban Catalyst is keen to work in Leeds and we are hopeful of still doing something in the city, ' he said.
'It was very pleased with the scheme and, if we can find another site, we can develop something along similar lines.
'We would love to do a building like this, ' he continued. 'It is a very interesting scheme and we understand from Carey Jones that the feedback from the public has been very positive, especially to the environmental factors such as the wind turbine.' 'We have not given up hope - I know that Urban Catalyst is very fond of the scheme, ' Affleck added.