The Hammers are set to move out of their Upton Park home and take up residence at the base of London 2012 in time for the 2016/17 campaign.
Tomkins is aware of how special the atmosphere at the Olympic Stadium promises to be, having formed part of Team GB last summer.
He is desperate to experience the thrill of competing on such a stage for his boyhood club, but acknowledges that he will first have to convince West Ham that he is deserving of fresh terms.
Tomkins told the Sunday Express: "It seems so far away right now but it will come soon. It should be a brilliant moment.
"My contract expires just before it happens but hopefully I will still be around because, just like all the fans, I am looking forward to that occasion.
"This has been my club since I was eight. It's hard to see me ever being anywhere else because I have been here so long, and my family are as excited as I am.
"To see their son potentially playing there makes them very proud. And being a local boy, I will be doubly proud to be there."
It remains to be seen who will make up the West Ham playing and coaching staff when they move into their new home, but Tomkins feels current coach Sam Allardyce should be given every chance to guide the club into an exciting new era.
He added: "He is doing a great job here.
"He got us promoted at the first time of asking and you can't ask for much more, really."