The much-travelled former England international returned to the east London club - where he made his name as a teenager - during this year's January transfer window.
The Hammers went on to finish the season 10th in the Premier League table, following their promotion from the Championship.
And he believes it is about time that the Upton Park side returned to the national stadium where they won three FA Cup finals and a European trophy between 1964 and 1980.
The 31-year-old former Chelsea and Liverpool midfielder said: "I think the ambition of the club at the moment is improvement.
"But for me personally, I would love to finish better than 10th but I would love to take this club to Wembley.
"At the end of the day, they are the days you remember in your career - it would be a massive achievement.
"You look at Swansea and Wigan last season and that is their day, we would like a bit of that because it has been such a long time since West Ham have been there, so that would be nice."