The former Spain Under-21 international was a regular last season as David Moyes initially got the Hammers out of danger, only for a knee injury to rule the player out until May.
West Ham soon slipped back into relegation trouble, though they ultimately survived in the Premier League by finishing 13th in the table.
The arrival of seven new signings at the London Stadium this summer, including central midfielder Jack Wilshere, has thrown Obiang's future into doubt.
According to Italian outlet La Repubblica, Sampdoria have submitted a £7m bid in the hope of bringing their former player back to Genoa this summer.
Obiang spent five years at the Serie A club before moving to West Ham in 2015 on a four-year deal.