Paul Burrell said he spoke to his parish priest about how a Christian woman and Muslim man might marry.
Mr Burrell worked for Diana for more than 10 years.
He also said that he
"connected all the princess's friends and all her world"
"at the hub of the wheel, everybody was at the spokes".
Mr Burrell said Diana told him that she had been more in love with Mr Khan than "any other man".
The "extremely serious relationship" had lasted for two years, he said, and Dr Khan had been a regular visitor to Kensington Palace until the couple parted in July 1997.
When asked by Ian Burnett QC, representing the inquest, whether she "contemplated" marriage with Mr Khan, the former butler replied: "Yes, she did.
"She asked me if it was possible to arrange a private marriage between her and Hasnat Khan."
However, it is not known whether Mr Khan was aware of these discussions.
Mr Burrell also said he had not been given the impression that her boyfriend, Dodi Al Fayed, was "the one".
He described Diana's relationship with Mr Al Fayed as
"a very new friendship which developed into something more".
He told the High Court in London that he did not believe the couple's romance had begun during a holiday on Mr Al Fayed's yacht at the end of July 1997.
Instead he thought it was only after their return that the pair became romantically linked.
Diana had taken a holiday on Mohamed Al Fayed's yacht, the Jonikal, with her sons, Princes William and Harry.
When asked by Mr Burnett about the early nature of the relationship, Mr Burnell replied:
"It was very fresh, new and exciting."
Mr Burnett also asked:
"By that stage had you any sense from the Princess that... to use a hackneyed phrase that has appeared in so many media reports, Dodi was 'the one'?"
Mr Burrell replied:
"No, I didn't have that impression.
Showered with gifts
"I certainly don't think the romance started on the first holiday. I think that would have been inappropriate with William and Harry being in attendance."
Mr Burrell also said a ring bought by Mr Fayed for the princess was
"not an engagement ring, it was a friendship band".
He said that to make sure no-one, including Mr Al Fayed, would be misled into thinking it was anything else, Diana wore it on the fourth finger of her right hand instead of on her left.
Mr Burrell said this was his idea, made to the excited princess as she was being showered with gifts of "very expensive" Bulgari jewellery by her new beau that included a necklace, earrings, a bracelet and a watch.
Mr Burrell said he told Diana:
"You know what is coming next. The next gift you are going to receive will be a ring and it could be misconstrued as an engagement ring.
'On the rebound'
"She said 'If he gave me a ring, what should I do with it?' and I said 'Put it on the fourth finger of your right hand and immediately he will see that it is a friendship ring, not an engagement ring' and that's when she said 'I need marriage like a rash'."
Mr Burrell said the couple were definitely not engaged and rubbished rumours that they planned to wed.
"This was only a 30-day relationship. The princess had just finished a long-term relationship with someone she had cared deeply about. I know that because I was there and saw it.
"And on the rebound from that relationship, (she) had met someone who was very kind, generous and spoiling. The princess enjoyed it."
He said that if Diana had got engaged she would have told close friend Lucia Flecha de Lima or "someone she trusted as much as me".
Coroner Lord Justice Scott Baker has previously said the jury may think Mr Burrell had unrivalled knowledge of intimate aspects of Diana's life as he "plainly had a close professional relationship with Diana."
Diana died along with her lover Dodi Al Fayed and their driver Henri Paul in a car crash in Paris in 1997.
Mr Burrell is likely to be questioned about a note from the princess to him in which she said that her husband Prince Charles was "planning an accident in my car".
He may also be asked about a conversation he had with the Queen in which he claims she warned him:
"There are powers at work in this country about which we have no knowledge."