The client for the £220m scheme, the National Institute for Research into Aquatic Habitats, plans to create the world's largest freshwater centre for the study of aquatic animals, and house it underneath Eden-style domes.
Two of the sites are in the north of England, one in the south and one in Northern Ireland. One of the sites is believed to be at St Helens, Merseyside.
The institute had planned to build the site outside Weston-super-Mare, near Bristol, but the plan was ditched earlier this year when it emerged that there was a funding shortfall. The local council had also expressed doubts over planning permission.
Steve La Thangue, a zoologist at the institute, said the site would be chosen based on two criteria.
He said: "As the centre is partly funded with public money, we have got to look for the best possible site in terms of infrastructure and aesthetic qualities. But we also want to build an institute that will last for the next 100 years; we don't want a tourist attraction that will fall apart in seven."
The centre will have public and private funding, although the amount of each will depend on which site is chosen. The project team is also in talks with hoteliers to build a five-star hotel and a 1500-seater conference centre as part of the development.
A final decision as to which site is used will be made by the end of the year, provided funding is in place.
The project team includes many of the people who were involved with the Eden Project in Cornwall. Grimshaw has drawn artists' impressions for the project and will be joined by engineers Anthony Hunt Associates and Arup, and QS Davis Langdon & Everest. The scheme is to be under the control of Ronald Murning, from Land Architects, who was project manager on the Eden Project.
The scheme will feature three domes called "biotopes", rather than biomes as at the Eden Project. Two of these structures will be used for aquatic research, with 150 aquariums using 20 million gallons of water. The third dome is to house a 5 million-gallon diving tank to replicate swimming in the wild.
La Thangue said the scheme would primarily be a research institute, with aquariums containing species from all over the world, but would also be used to educate visitors.
A spokesperson for the client said the research centre would aim to "lift the lid off science".
He said: "The centre will be world class and a world first. It will give the public the opportunity to see marine life from all around the world, and offer a safe environment to see species that may be under threat in their natural environments."