The royal is dating 24-year-old socialite Cressida Bonas and there has been speculation he is ready to settle down with her.
In February the couple put on an affectionate display while skiing in Switzerland with Harry's uncle Prince Andrew and his ex-wife Sarah Ferguson. The divorced couple's daughters Beatrice and Eugenie were also there, with Eugenie and Cressida good friends.
"I'm told they talked of marriage in Switzerland this year. Fergie was urging him to propose, but H wouldn't go that far," a source explains in upcoming book Harry: The People's Prince by Chris Hutchins, an extract of which has been published in British newspaper The Daily Mail.
"That said, he's seen how happy marriage has made his brother and I think he wants some of that. I'm also informed that Cressida's mother has told Eugenie she'd love to see them settle down together, but Cressida won't be rushed any more than he will."
The tome is due out on April 25 and includes an in-depth look into Harry's romantic life.
He famously dated Chelsy Davy on-and-off until 2010, with the relationship said to have ended because Chelsy didn't want to enter into such a public life.
Close friends of the 28-year-old prince apparently feel she is the love of his life, with one even claiming the relationship could be rekindled in the future.
"Don't write Chelsy off," the insider said. "She was the love of his life for seven years, and it wouldn't surprise me if she didn't re-emerge at some point in the not-too-distant future.
"I think they love each other and eventually they will get back together. In fact - and she'll hate me for saying this - I believe they will marry once she is convinced, of course, that his wandering eye days are over."
The new book also includes an account from a woman known as Margaret, who briefly dated Harry while he was at school Eton College. She has not spoken about their dalliance in the past and met the royal when he came into the shop where she worked.