Nolan was released by the Hammers last month, but he still predicts that the side will enjoy a productive campaign with Slaven Bilic at the helm.
At the moment, West Ham are in fifth place in the Premier League table, following a 2-0 win over Newcastle United in their most recent fixture, and Nolan has seen enough from them already to suggest that they have the quality to finish in the upper echelons of the top-flight standings.
"They have a strong chance of a top-10 finish and I think that'll be a good season for them, with them moving into the Olympic Stadium next year," he told Sky Sports.
The positivity around West Ham at the moment stems from what has been a very impressive start, with the Hammers triumphing over Liverpool and Arsenal prior to beating Newcastle.
Although home defeats against Bournemouth and Leicester City have stopped them from having a perfect record, there has still been enough on display to take encouragement from.
The Hammers appear to have bought very well over the summer, with Dimitri Payet in particular making a very bright start to life at Upton Park.
The Frenchman has scored three goals in his first five games, and he appears to be one of the most astute additions made during the recent transfer window.