Neither has spoken about the speculation, with Jessica previously saying she pays no attention to gossip.
They have been seen out together lots recently, and are thought to be happy together.
However, Jessica is keen to tie the knot, and has reportedly asked Justin to pop the question by the end of the year.
"Jessica wants to settle down and have children," a source told National Enquirer. "Every time the subject of marriage or engagement came up this year, Justin said he needed until Christmas. Jessica has made it crystal clear that she expects him to honour his promise."
Justin is said to be contemplating proposing, but is not sure he is ready to settle down yet.
The 29-year-old has even consulted his pals about the quandary, who are said to have told him he is "crazy" not to have asked his 28-year-old girlfriend to marry him already.
