The French Rugby Federation says it has also held conversations with Lions officials about warm-up matches before the 2027 and 2029 tours.
France has been flagged as a future series option due to the strength of their national and club sides, the popularity of the sport among the French public, and the relative affordability for travelling Lions fans.
FFR vice-president Abdelatif Benazzi said: “I think we can build something for the long term. We start with this, but I don’t want it to be just one shot.”
The Lions have not played France since 1989 in a fixture arranged to celebrate 200 years since the French Revolution.
When asked about the prospect, Calveley said: “You can certainly understand why people will get excited about that sort of concept [a series in France].
“What’s not to like about some of those wonderful clubs you could play against and some of those wonderful venues in the summer as well?”
