Southampton, Portsmouth and Isle of Wight councils applied to the government in October to create an authority to boost economic growth.
They said they had been allocated £900m over 30 years by the government.
Portsmouth Council leader Donna Jones said the money now appeared to have been lost because of opposition by Hampshire County Council.
Ms Jones said it was "highly unlikely" that the government would agree the deal, because "there isn't consensus".
The situation was discussed at a meeting at Westminster on Wednesday involving Hampshire MPs and council leaders.
The new Isle of Wight Council leader Dave Stewart said he confirmed to the meeting that his recently-elected Conservative administration would not support the existing bid.
Isle of Wight Conservatives had previously said the island's needs "could easily be overridden" by Southampton and Portsmouth.
Hampshire County Council leader Roy Perry said: "I'm not surprised that the deal is now dead.
"It would not have helped the local economy and would have led to the dismantling of vital county-wide services - such as transport, health and social care."
Keith House, the leader of Eastleigh Borough Council, which had been in talks to join the Solent Combined Authority (SCA), said the bid was "almost certainly dead", but Fareham Borough Council leader Sean Woodward urged the government to "press ahead" with the deal.
The Department for Communities and Local Government said devolution applications should be accompanied by "local support", but did not say whether the Solent bid had been refused.
The Conservative MP for Havant, Alan Mak, said: "The money is still very much there.
"This is an opportunity for the council leaders to come forward with new proposals that are viable."
A deal to set up a new authority for the Solent area is "almost certainly dead", council leaders have said.