The 23-year-old defender has been very impressive for the Hammers all season and Team GB coach Stuart Pearce is a known admirer of the centre-back.
Tomkins has admitted the he would be delighted to make the final cut, should his name be included on the squad list of 18 to be announced in the first week of July.
“I would be very proud to represent Great Britain in the Olympics, as I am sure the other lads would be as well. It would be a great honour. I have always been really proud to represent my country (England) before and this would be another proud moment for me.
“At the moment, all we know is that we could be selected but there is process to go through first so we don’t know if we would be chosen, but to be in the hat is a great thing.
“With the Olympics also being in London, it gives it an extra attraction - as everyone knows, it is right on our doorstep and I am sure our fans are excited about the Olympics being here as well, it should be an exciting time for London. Being a London club, it is right in our community and that can only be a good thing.”