Trump has previously criticised NATO, calling it "obsolete" in an interview earlier this year.
Security and IT systems at the $1.2-billion headquarters in the Belgian capital are behind schedule and so the transatlantic military alliance will only properly move in come September, sources told AFP.
Trump has previously criticised NATO, calling it "obsolete" in an interview earlier this year and pressing the rest of the 28-nation group to commit more money to it.
A source close to the matter told AFP that NATO aimed to inaugurate its new building after the summer holidays, "in my view more like the end of September."
Asked for comment, NATO spokeswoman Oana Lungescu told AFP: "On the summit venue, we aim to hold it at the new headquarters."
"The move to the new NATO headquarters has started and it's due to be completed later this year," she said, describing it as a "complex logistical undertaking" involving NATO staff and delegations from the 28 allies.
"The new IT and security systems in the building are highly complex and we are slightly behind schedule in making all of them fully operational."
Lungescu did not give a date.
The supplier responsible for delivering the network infrastructure has still not delivered it to the alliance, which has in turn pushed back security tests, the source close to the matter said.
The new NATO HQ, built in a distinctive double lightning bolt shape, will house 4,000 staff and diplomats from the 28 member countries.
Built just over the road from the current 1960s-era headquarters near Brussels airport, it had been scheduled to open in the first quarter of 2017.
The White House confirmed last week that Trump will attend the May summit, easing doubts in Europe about the new US president's commitment to the bloc.
Trump expressed "strong support for NATO" in a phone call with the alliance's Norwegian chief Jens Stoltenberg but also urged European members to pitch in more to ease the defence spending burden.
Trump's apparent coolness towards the alliance has been particularly alarming for some member nations given his friendly stance towards Russia, which NATO has described as being increasingly assertive in the wake of its seizure of Crimea from Ukraine in 2014.