Obinna is at West Ham on a season-long loan deal from Inter Milan after falling down the pecking order at the European champions.
The Nigeria international has caught the eye during his first two outings for West Ham and the 23-year-old claims he would be open to the idea of staying at the club.
"I wanted to try playing in the Premier League because I thought it was a style of football that seemed right for me," Obinna told the Daily Mirror.
"There is also a possibility that my move could be made a permanent one.
"I'm happy to be a West Ham player.
"I believe we have to work hard to take West Ham where it belongs."