A senior source has said that the US leader wants the UK to cough up more than two percent of its GDP in a bid to get Europe as a whole to contribute to the alliance.
Britain is one of the few member states that achieves Nato’s target of opening two percent of its GDP on defence.
One Government source told The Times: “They will want the prime minister to be able to give a very clear direction of what the UK is bringing to the table.
“There is a feeling that the Americans expect more from the UK as a partner of choice.”
During the presidential campaign, Trump described Nato as “obsolete and disproportionately too expensive”.
And after the G7 Summit in Canada last weekend, the US President fired off tweets venting anger at his Nato allies.
He wrote: “The US pays close to the entire cost of Nato-protecting many of these same countries that rip us off on trade, they pay only a fraction of the cost and laugh.
“Germany pays one percent slowly of GDP towards Nato, while we pay four percent of a much larger GDP. Does anybody believe that makes sense?
“We protect Europe which is good at great financial loss, and then get unfairly clobbered on trade. Change is coming.”
Theresa May is due to discuss the conclusions of the defence review to the leaders of Nato’s 28 other member states at the defence union’s summit in Brussels in July.
The Ministry of Defence (MoD) is modernising the country’s defence currently and Chancellor Philip Hammond must seek more funds for defence.
In May, Mr Trump said that Nato allies that do no meet the organisation’s defence spending targets would be “dealt” with and singled out Germany as not doing enough.
The MoD have said that any discussions on the outcome of modernising the defence programme would be “pure speculation” before they share “headline conclusions”.