In April it emerged that a council-owned car park was set to be sold and used for older people's accommodation.
Last year the Shoreline Housing Partnership, which owned six nearby high rise blocks, made a decision to demolish the buildings, moving hundreds of people out.
Shoreline now say the new development is "not financially feasible".
Designs for 46 one and two-bedroom apartments were presented to residents for consultation in January.
Tony Bramley, of Shoreline, said: "We thoroughly explored this proposal [for the so-called Nelson Court] commissioning local architects to draw up designs, looking at prospective locations and carrying out consultation with affected high rise residents.
"While we've always been clear that funding and a location would need to be sought, we genuinely hoped that we would be able to make it work but it's simply not financially feasible and we've been unable to gain the level of funding required to support the scheme something that is particularly challenging at a time when public subsidy is so tight.
"This may come as a disappointment to some residents but we remain committed to helping them find accommodation that meets their needs and preferences."
Shoreline said it had appointed a firm to lead on proposals for the regeneration of the cleared site and immediate surrounding area.
Plans to build accommodation for older people in Grimsby have been abandoned because of a lack of funding.