The couple met in early 2011 and announced their engagement in March 2012.
On Monday (August 27), MediaTakeout claimed that Rose is pregnant.
A source has now told RadarOnline: "Amber and Wiz unexpectedly got pregnant, but they're really happy to be starting a family together.
"Amber's already had to make some big lifestyle changes, like not smoking cigarettes any more. As a model she's used to having a thin waist, so this is going to be an adjustment for her."
The couple are allegedly due to welcome their child in January and could move up their wedding date to this October.
Rose, who dated Kanye West, previously revealed that she fell in love with Khalifa after they spoke on Twitter.
"I love everything about him. That's my baby. He is my little angel. I love him," Rose said about Khalifa.
Listen to Amber Rose and Wiz Khalifa's track 'Fame' below: