The Spanish midfielder joined the 'Hammers' in 2015 from Sampdoria, and has been a regular in the team since his arrival, making 87 appearances in all competitions.
However, the club have looked to revamp their squad over the transfer window with the signings of Jack Wilshere, Felipe Anderson and Andriy Yarmolenko in the middle of the park.
As a result, Obiang is unlikely to get as much game time under Manuel Pellegrini as he has done in recent years, and so could seek a move elsewhere.
According to the 'Daily Mail', his most likely option is his former team in Italy, with talks over the transfer in fairly advanced stages.
West Ham have made a number of additions so far this summer, and are not thought to have finished their activity in the market with there still being a possibility of players leaving and coming in to the club.