The striker-turned-pundit says the Hammers should qualify for the top four at the expense of a 'bigger' club.
In their first season under the management of Slaven Bilic and their final year at their traditional Upton Park home before relocating to the Olympic Stadium, the Hammers are currently fifth in the Premier League table, just a point off a place in the top four.
The Irons' fine form, driven by such signings as Dimitri Payet and Manuel Lanzini, has led to a first-ever qualification for Europe's premier competition emerge as a real possibility.
In a season which has seen the recent dominance of the top four positions by clubs such as Chelsea and Manchester United broken up by title-challenging Leicester City and Tottenham Hotspur, Cundy is adamant that West Ham also deserve to be there come the end of the season.
He told Football Fanzone: "West Ham are as good as any side looking to play in the Champions League next season and are a very good shout. They are a very good side with players that can win matches. Their last 2 games have seen them go away to Old Trafford and Stamford Bridge picking up draws at both but coming away disappointed, which says a lot.
"The thing that stands in their favour is that of all the teams looking to break into the top 4, they are the most consistent. They play at a high level every week unlike lets say a Manchester United, where you wonder what team will turn up.
"For me West Ham have to be favourites [to finish fourth], and a first foray in the Champions League would be a well deserved reward for a team that have impressed against the big boys this season and are about to move into a new 60,000-seater stadium."
Breaking into the top four would come at the best possible time for the London club ahead of their move into the Olympic Stadium for the start of next season, and would allow them to attract more players of the calibre of Payet.
Even if they ultimately fall short of that goal, they have another opportunity to qualify for Europe with triumph in the FA Cup, with a semi-final against Everton waiting if they can see off United in the quarter-final replay at Upton Park next month.