"Given all the financial pressures across the whole of the public sector, all the things the Government has to do and wants to pay for, and all the pressures in different areas, I just think the idea that somehow, out of thin air, we can carve a multibillion pocket to pay for this, that is not financially realistic," he said.
"We are in a position where the costs of the successor have to be paid for from within the Ministry of Defence budget. There is no magic pot of money that is going to be created out of thin air to go on top of that. As a Government, we have been very clear about that. Certainly myself and the Chancellor."
Mr Alexander went on: "I would expect we will be able to set out serious, credible arguments and potential alternatives.
"I hope (the review) will open up a wide debate, in the public, among experts and the community, around the approach we take to nuclear deterrence."
The Government is spending around £1.4 billion on early design work for Trident replacement submarines, but the final decision about whether to go ahead - known as the "main gate" - is not due until after the general election.