The England midfielder, who came through the Hammers youth ranks, moved back to Upton Park in January and has a contract until 2015.
West Ham announced on Friday that they will move from Upton Park to a reconfigured Olympic Stadium for the 2016-17 season.
And Cole said: “To be still here in 2016, and have my family come and watch me in a sold-out stadium, that would be a very proud moment for me.
“I’ll be 34 then. I keep myself fit and want to play as long as I can because I love playing and I’d like to be playing here.”