Tuesday evening will see Burnham's first state banquet since becoming prime minister. He will take one of the places of honour in St George's Hall, on a lavishly decorated table that can seat about 160 guests.
Burnham previously spoke to the Sultan in July, when they discussed efforts to open the Strait of Hormuz to shipping, and the prime minister said he was grateful for Oman's attempts at mediation.
The guest list does not include non-working royals, like the Duke and Duchess of Sussex.
An interview with Prince Harry with GQ was released as the state visit was getting under way.
He talked about his complicated relationship with his father and brother - recognising that it was something that was "massively relatable" for the public.
"Some people don't want it to work out," he said. "I want it to work out.
"With everything else that's going on in the world, the most important thing is to reconcile - that's the key point... scars stick around forever."
In the interview, which took place in New York, he said he would "encourage everybody" to let go of the past.
"If there's certain things from the past that are still affecting you every day, that's harder to let go of," he told GQ.
"But, for me, there's enough drama in the world and enough drama in people's lives to continue with issues with family."