Slaven Bilic's side have mounted a fine top-four bid so far, with the Hammers fifth in the Premier League table, one point behind fourth-placed Manchester City as the battle hots up.
The Irons are also in contention to end their 36-year wait for an FA Cup title as they prepare to host Manchester United next month in a quarter-final replay, after the previous clash finished 1-1.
Furthermore, this is West Ham's final season at the Boleyn Ground, which they have occupied for 112 years, and Sinclair is admittedly enamoured with the idea of their new home hosting some of Europe's elite next term.
Champions league at the new stadium https://t.co/qCzXRDMp5P— Trevor Sinclair (@trevor8sinclair) March 22, 2016
Failing to secure a top-four finish or the FA Cup would be a bitter blow to Bilic, but he could still yet secure Europa League qualification if they come fifth in the table.
Their next two Premier League games are at Upton Park, against Crystal Palace and Arsenal respectively.