Silverman, 35, who settled a divorce this week with former husband Andrew, has told friends that she hopes to join up with Cowell, reported Daily Mirror.
Cowell, 53, will be in London this weekend but is due to jet back to the South of France, where he has been holidaying on Slipstream, next week.
"Lauren, who is pregnant with Simon's baby, settled a messy divorce this week and expects to spend time with the multi-millionaire on the charter. She and boss Simon, who allegedly began having an affair four years ago, are still very much together," a source said.