The 29-year-old joined the Hammers from Juventus in 2015 and was expected to emerge as a key figure at the London Stadium.
However, he missed a considerable part of last season with a knee injury, but played the full 90 minutes in the final-day victory at Burnley.
Not a regular at Juventus, Ogbonna was still rated highly and it is unclear if the Hammers would be willing to sell him.
According to Il Secolo XIX, Sampdoria are showing an interest in the West Ham defender and could look to take him back to Italy ahead of the start of the new season.