In the church of Santa Maria in Cosmedin, Rome
Whose Body? There were several Saint Valentines, but their relics are elsewhere:
"Valentine of Rome was a priest in Rome who suffered martyrdom
about AD 269 and was buried on the Via Flaminia. His relics are at the
Church of Saint Praxed in Rome, and at Whitefriar Street Carmelite
Church in Dublin, Ireland.
Valentine of Terni became bishop of Interamna (modern Terni) about AD 197 and is said to have been killed during the persecution of Emperor Aurelian. He is also buried on the Via Flaminia, but in a different location than Valentine of Rome. His relics are at the Basilica of Saint Valentine in Terni (Basilica di San Valentino).
The Catholic Encyclopedia also speaks of a third saint named Valentine who was mentioned in early martyrologies under date of February 14. He was martyred in Africa with a number of companions, but nothing more is known about him"
Vicipaedia in linguam anglorum
A lot of 'relics' in Roman churches may have come from burials- not necessarially Christian- in the network of catacombs underlying many of the main roads in the city.