The 'Hobbit' actor - who has five-year-old son Flynn from his former marriage to Miranda Kerr - is said to be keen to "settle down" with the 31-year-old singer just months after they were first romantically linked to each other in January.
A source said: "[They are] not engaged yet, but seem to be heading that way.
"He would love to settle down with Katy and have more kids. He hasn't been this serious about a girl since Miranda.
"[Orlando] always gushes about Katy and thinks she is amazing in a million ways."
But the 'Roar' hitmaker, whose divorce from comedian Russell Brand was finalized in 2012, is not thought to be quite as keen as the 39-year-old actor - who divorced Miranda in 2013 - to tie the knot again.
The source explained: "She's not going to rashly make a huge commitment like marriage again unless she thinks it's absolutely right."
The couple - who recently hit the headlines after they were pictured paddleboarding together on holiday, during which the Hollywood hunk was completely naked - are said to be in a "serious" relationship and also manage to have their own space.
The source added to PEOPLE: "They've been getting along really well.
"Katy gives him space, and they're both pretty independent. They are serious about each other and their relationship."
Miranda recently got engaged to Snapchat founder Evan Spiegel, and Orlando congratulated her.
A source said at the time: "Orlando is happy for Miranda.
"He spoke with and congratulated her.
"Orlando knows that Evan treats Flynn well so that's all that matters to him."