But even Allardyce found it difficult to justify a place in his team for the midfielder last season.
Instead the ex-Newcastle United man was restricted to a bit part role and finished with his worst ever goal return in a Premier League season of one.
Speculation has been rife that Nolan will be moved on this summer now that his trusted manager has departed.
But the 33-year-old had been notable by his silence since Allardyce's departure in May.
Now speaking to West Ham's official website Nolan has admitted he is yet to discuss the future with the new man in charge at the Boleyn Ground.
"This is the second day we've worked with him and seen him," Nolan told whufc.com.
"We've not had a sit down chat yet, so I don't know too much about him or what is expected this season but he's had a few quiet words with us in meetings."
Kevin Nolan, West Ham scapegoat?
Nolan has became something of a scapegoat among Hammers fans as West Ham's best ever start to a Premier League season faltered badly in 2015.
Cruelly labelled 'Allardyce's son' by some supporters, Nolan's popularity has waned despite helping lead the club back into the top tier of English football in 2012 and re-establishing themselves as a top flight force since.
In a recent HITC.com poll asking who fans wanted as the club's captain next season, Nolan registered just 11 votes (one per cent) from nearly 1,000 cast.
New manager will have his own ideas
Bilic will have his own ideas of how he wants to set his team up and has a preference for quick sharp passing through the midfield at pace.
That may not suit Nolan's game, which is more about feeding off knockdowns in the box from the likes of Andy Carroll.
The club have made their priorities clear already this summer where they think the team needs strengthening by signing two midfielders in the shape of Spanish Under 21 international Pedro Obiang and France star Dimitri Payet while Alex Song is expected to follow in the coming days - as per the Daily Mail.