The UK government said on Thursday it was confident that the deal to secure the future of a US-UK military base on the Indian Ocean island of Diego Garcia would be ratified.
Prime Minister Keir Starmer wants to finalise an October political agreement that hands Mauritius sovereignty of the Chagos Islands while securing a 99-year lease on the base.
The deal still needs to be ratified by both sides.
Ramgoolam, who won an election this month, has expressed doubts about the agreement.
He told parliament on Thursday his new cabinet would be able to consider the outcome of the review.
The UK's foreign ministry declined to comment.
UK foreign minister David Lammy said earlier this week he was confident the deal would go through, adding that the US intelligence agencies, State Department and Pentagon had all welcomed it.
He said the UK was happy to give the new Mauritius government time to examine the details.
US President Joe Biden supported the deal when it was announced but it could be challenged by the next US administration after Donald Trump is sworn in as president in January.
Trump's pick for secretary of state, Marco Rubio, has said the deal poses a serious threat to US security by ceding the archipelago - with its strategic base used by US long-range bombers as well as warships - to a country allied with China.
When Mauritius became independent in the 1960s, the UK retained control of the Chagos Islands, and forcibly displaced up to 2000 people in the 1970s to make way for the base.
The UK said last month it would hand over the islands, after years of sometimes acrimonious negotiations.
But many of the exiled Chagossians say they were not involved in the negotiations and cannot endorse it.
Olivier Bancoult from the Chagos Refugees Group, which defends the rights of Chagossians, said he hoped the review would be done quickly.
"There is a need to correct injustice inflicted on the Chagossian population," Bancoult told Reuters.
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