The reality TV mogul welcomed his first son, Eric, with the socialite in February and his 'Britain's Got Talent' co-judge is sure he will want to expand his family further.
She told Hello! magazine: ''I do [think they will get married]. And I think they'll have more children too, because he loves it.
''Simon definitely should ask Lauren to marry him. He shouldn't let her get away. Lauren's such a good influence on him.''
Amanda also thinks the notoriously picky TV star has found someone who will stand up to him in Lauren, and that she is someone who is unlikely to let him win all their arguments.
She added: ''He's met his match in Lauren, 100 per cent.''
Lauren has previously said she and Simon are in no rush to tie the knot and are simply enjoying parenthood.
The 37-year-old - who was recently granted a divorce from millionaire ex-husband Andrew Silverman, the father of her eight-year-old son Adam - said: ''Of course we will get married eventually, but not yet.''
Meanwhile, she thinks Eric looks more like his famous father than her, and isn't surprised by how well Simon has taken to being a father.
She said: ''I think he's absolutely adorable! He does look a lot like his dad. He looks nothing like me.
''I'm not surprised, I knew he would be an amazing father. He's an amazing guy with a good heart. Sometimes when you get in a situation, you rise to the occasion and he really has. Simon's an amazing dad. It's so cute when I see them together. I just love it.''
This Doctor won't be saying 'goodbye' in the same way as those who have left the series in recent years.