The pope, who is by tradition the owner of the cloth, said he hoped to be able to visit the Shroud in the northern Italian city where it is normally kept rolled up in an ornate silver box, "if the Lord grants me life and health".
The last time the Shroud was put on public display was for the Catholic jubilee year in 2000.
The cloth measuring 4.4 by 1.2 metres (14.5 by 3.9 feet), bears the inexplicable image - eerily reversed like a photographic negative - of a crucified man.
The cloth shows the back and front of a bearded man with long hair, his arms crossed on his chest, while the entire cloth is marked by what appears to be rivulets of blood from wounds in the wrists, feet and side.
It was shown only four times in the 20th century.
In 1988, carbon dating tests by laboratories in England, Switzerland and the United States indicated that the Shroud dated from between 1260 and 1390 - implying it was a fake and could not be Christ's burial cloth.
But scientists are at a loss to explain how the image was left on the cloth. Most agree it could not have been painted or printed and some have said the 1988 tests may have been faulty and results corrupted by bacteria encrusted over the centuries.
Some have called for new tests using techniques not available in 1988.
The history of the Shroud is long and controversial.
After surfacing in the Middle East and France, it was brought by Italy's former royal family, the Savoys, to their seat in Turin in 1578.
In 1983 ex-King Umberto II bequeathed it to the late Pope John Paul, Benedict's predecessor.
The Shroud narrowly escaped destruction in 1997 when a fire ravaged the Guarini Chapel of the Turin cathedral where it is held. The cloth was saved by a fireman who risked his life.
The Catholic Church does not claim the Shroud is authentic nor that it is a matter of faith, but says it should be a powerful reminder of Christ's passion.
When he viewed the Shroud in 1998, the late Pope John Paul called on the scientific community to continue research to find adequate answers to the questions linked to the linen.
