The 'Stay With Me' hitmaker has admitted he is so ''obsessed'' with the couple - who announced their engagement earlier this week - that he has been dreaming of the chance to provide the musical entertainment at their nuptials in May next year.
He said: ''I'm obsessed. I want to sing at the wedding. Oh my God I'd love to, it would be a dream.''
Sam, 25, is a big fan of the 33-year-old royal, and remembers meeting him at the premiere of James Bond movie 'Spectre', for which Sam sang the theme song 'Writings On The Wall'.
He added: ''I met Harry once, at the James Bond premiere in the Royal Albert Hall, and he also did this amazing speech at the Attitude Awards, and it was really, really beautiful to see that.''
It isn't just Harry and Meghan, 36, that the 'Too Good At Goodbyes' singer is a fan of either, as he also recalls ''running around London with a flag'' in 2011 when Harry's brother Prince William married Catherine, Duchess of Cambridge.
He revealed: ''I woke up at 6am, downed a bottle of wine and went and sat in Hyde Park. I was wasted the whole day, running around London with a flag. I was just screaming when she walked out in that dress.''
Seeing his favourite royals gear up for their big day has got Sam - who is in a relationship with '13 Reasons Why' star Brandon Flynn - thinking about his own future wedding, though he admits the special occasion is a long way off yet.
Speaking to The Sun newspaper, he said: ''I'd love to get married one day. But I'd want to have the wedding after being with someone for a long, long, long time. I wouldn't have a traditional ceremony. I want to have a wedding in Italy, with loads of pasta and wine. Nothing very formal, everyone in linen suits.''
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