The Pope is due to visit the UK in September.
Mark Damazer, the controller of Radio 4, revealed that Thompson met senior Vatican officials in Rome earlier this month and is personally leading the negotiations with them.
If it is not possible for the Pope to record for Thought for the Day during his UK visit, the BBC may persuade him to make a longer contribution that could be aired elsewhere in the schedule.
However, secular groups have reacted angrily to Thompson's efforts. Since the message by the Pope has been unprecedented in the history of the BBC, they fear that the Papal visit will be exploited by the Vatican as a great media opportunity.
Dr Rowan Williams, the Archbishop of Canterbury, Rabbi Lionel Blue and the Bishop of Southwark have been the regular contributors to the three-minute slot that is broadcast around 7.45am.