Ms May is seeking to emphasise Britain's contribution to European security through training, cyber security and martime patrols as she begins the Brexit divorce process.
The UK defence ministry said it was working with Germany "on a joint vision statement on future co-operation."
The German defence ministry confirmed to The Financial Times it was working on joint projects.
“Independent of the effects of Brexit, Great Britain remains a strong partner and ally in Nato and also bilaterally,” it told the paper.
Sir Michael Fallon, UK defence secretary, has reportedly been speaking to several EU countries about building military links.
It comes as British troops were deployed to Estonia as part of a Nato plan to deter Russian aggression in the Baltics.
The troops are due to be stationed in the country in one of the biggest deployments to Eastern Europe since the Cold War.
The Royal Navy's latest helicopter, the Wildcat, will also be deployed from a German frigate and take part in operations in the Mediterranean next year.
The US President also suggested Germany should pay the United States more for defending it.
After a video appeared to show Mr Trump ignoring Ms Merkel's request to shake hands at a photo opportunity, he tweeted: “Despite what you have heard from the FAKE NEWS, I had a GREAT meeting with German Chancellor Angela Merkel.
“Nevertheless, Germany owes vast sums of money to NATO & the United States must be paid more for the powerful, and very expensive, defense it provides to Germany!”
Germany does not currently reach the alliance's benchmark of spending at least 2 per cent of GDP on defence, currently spending 1.23 per cent.
However, Ms Merkel said Berlin is aiming to increase the amount it contributes.
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