"That seems to me to be an excellent idea," Portuguese cardinal Jose Saraiva Martins was quoted as telling the Quotidiano Nazionale daily's Monday edition.
"It has never been done but the Church has always encouraged sport as a vehicle for healthy values."
Archery, he said could be held in the Vatican's gardens or in the little-used expanses at the Pope's summer residence at Castelgandolfo, to the south east of Rome.
The cardinal's eye-catching suggestion came as Italy officially announced a Rome-led bid for the Games, which the capital previously hosted in 1960.
The Olympic stadium and swimming complex built for the 1960 games are expected to be upgraded to host athletics and the acquatic events if Italy succeeds in its bid.
Other events are to be spread around the country with the sailing notably expected to be off Sardinia, the island that is a firm favourite with millionaire yacht owners.