Asked whether the former US president would come with his wife to the ceremony next year, the Prince said: “I don’t know about that.”
Prince Harry is close to the Obamas following their collaboration during the Invictus Games, a sporting event for war veterans, in September.
Speaking to BBC Radio 4’s Today programme, which he was guest editing, Prince Harry discussed whether the ex-Democrat president would be invited to his wedding, saying: “I don’t know about that. We haven’t put the invites or the guest-list together yet.
“So who knows whether he’s going to be invited or not? I wouldn’t want to ruin that surprise.”
He likened the challenge he faces with the guest-list, to that facing every couple looking to get married and said the decision was not all his, but also his fiancé’s, adding: “That’s why I’m keeping quiet.”
However, the Prince did say he had a close relationship with Mr Obama, explaining that he was the “easiest” interview to get for his special edition of the Today programme.
He went on: “We share the same kind of mind-set and the outlook on the charitable sector, on foundations and mainly on the youth of today.”
A report in The Sun earlier this week quoted a “senior government source”, saying that Prince Harry had “made it clear” he wanted the Obamas at the wedding.
The source reportedly said: “Trump could react very badly if the Obamas get to a royal wedding before he has had a chance to meet the Queen.”
Mr Trump was invited on an official state visit — including a meeting with the Queen — to the UK earlier this year by Theresa May, on a White House visit in which she was pictured holding hands with the President.
While Downing Street insists the invitation still stands, it is yet to be scheduled and has led to reports that Buckingham Palace was unhappy at the idea of the negative publicity Mr Trump may bring to the monarch.
Promises of demonstrations if the President sets foot in the UK have been stiffened by a series of Twitter interventions by Mr Trump in British affairs, including one in which he criticised the UK’s response to terror attacks and London’s Muslim mayor, Sadiq Khan.
Most recently, he re-tweeted racist videos from far-right group Britain First, drawing public criticism from Downing Street.
Mr Trump is expected to make a fleeting visit to the UK in February to open the new US Embassy in London.
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