The Hammers marked their return to the top flight last campaign by securing 10th position in the table.
"We have to have our ambition and we know the project of the club, so we need to work to try to finish near the top," Diame told the club's official website.
"We are going to try to give our best and make sure to do better than the last season. I feel a top-eight finish is achieveable, of course. Why not?"
The Hammers start the league campaign at home to newly-promoted Cardiff City on August 17.