Smiling, the 36-year-old quipped: "You'd have to ask him that.
The couple seem relaxed about the topic of marriage
The couple were in good spirits when the topic came up after a night out in Hollywood with Strictly Coming Dancing judge Bruno Tonioli and Lauren's friend Rachel Roy. Simon has previously introduced her to another pal, Louis Walsh.
This week, much to Lauren's shock, they were also asked if the father-to-be planned to have the birth filmed.
To which he replied: 'Am I going to videotape it (the birth), you'd have to ask Lauren...' Prompting her to exclaim: 'What?!'
Simon seems to be enjoying teasing journalists about the pregnancy. He previously confessed to having no idea what birth preparation classes when asked if he would attend with his girlfriend.
However, behind the playful attitude the impresario has given his full support to Lauren, who has a seven-year-old son with her former husband Andrew.
The 53-year-old has spoken of his joy at seeing a scan of his unborn baby boy, saying that fatherhood was a "fantastic" prospect at this time of life.
Simon has given Lauren his full support and introduced her to friends like Louis Walsh, pictured
In an interview with the US presenter Ryan Seacrest, he also hinted that marriage was on the cards. "I wouldn't expect Lauren to be a single mother ," he said.
Simon has come close to tying in the knot in the past. In 2010, he was engaged to make up artist Mezhgan Hussainy. From the outset of that romance his mother Julie had doubts that her son would ever make the trip up the aisle.
When asked if she had an outfit in mind for the big day, she replied: ” How can you buy an outfit for a wedding with no date or venue?’"
He also lived with entertainment reporter Terri Seymour – but the relationship came under pressure apparently because of his reluctance to settle down with a family.
This week another past girlfriend Sinitta has been in the news after responding to reports that she terminated a pregnancy with him.