Reid, who moved to Upton Park from Danish side Midtjylland 2010, played a starring role as the Hammers regained Premier League status.
The 25-year-old was instrumental at the heart of West Ham's defence as they beat Blackpool in the 2012 Championship play-off final at Wembley to return to the top flight.
Following West Ham's 2-0 victory over Burnley on Tuesday evening, which saw them reach the Capital One Cup quarter-finals, Reid is targeting a return to the national stadium.
"I think a good season for West Ham would be having a good cup run and getting to the final," he told the Daily Mirror after securing a last-eight tie against Tottenham.
"It would be nice to get back to Wembley. We've played there once in the play-off finals and it was a good day out.
"We are getting closer but it is going to be difficult."
Recent performances against some of the top European forwards in the Premier League have caught the eye of plenty, with rumours claiming Arsenal manager Arsene Wenger is preparing a January bid for the defender.
However, Reid refuses to get carried away with the speculation as he focuses on leading New Zealand to Brazil for the 2014 World Cup, with a crucial play-off against Mexico in two weeks' time.
"Obviously as captain of the New Zealand side I would love to take them back to another World Cup and it would be brilliant for me personally," he added.
"I would love to play in Brazil. I have been fortunate enough to play at one World Cup and would love the chance to do it again.
"When we were playing in South Africa in 2010 the streets were absolutely packed and it was 3am. The stadium sold out in a week and it will be a really good atmosphere there."