This comes after the couple were spotted hand-in-hand after enjoying a dinner date at Soho House, the private members' club in West London where they met last year.
The 35-year-old actress has reportedly 'virtually moved in' to Prince Harry's cottage in Kensington Palace in recent weeks, according to one friend.
One friend of Miss Markle reportedly told The Sun when she is not filming the US legal drama Suits in Toronto, the actress spends her free time with Harry.
The source added: 'They've taken things to the next level. They're practically living together.
'She cooks for him, he pops out to the gym and they're just enjoying hanging out.
'Meg has always enjoyed spending time in London, but she's really putting down roots.'
One of Meghan Markle's closes friends, Canadian actor Patrick J. Adams has given her relationship with Prince Harry the seal of approval.
Earlier this week Adams, who plays Meghan's on-screen fiancé Mike Ross, spoke candidly about the royal romance.
In a video interview with E! News' Erin Lim the star said he is 'super excited' for Meghan and revealed that if anyone can deal with it, then it's Meghan.