Alan Devonshire is sure the Hammers will continue to progress with manager Sam Allardyce at the helm.
The West Ham United legend was impressed with his old Club's efforts last season to secure a tenth place finish in the Barclays Premier League.
He is sure they are not finished there, and that with a couple of additions this summer, could aim even higher in 2013/14.
WATCH THE INTERVIEW WITH ALAN ON WEST HAM TV HERE
He told West Ham TV: "I thought we'd do okay last season. We finished tenth, and hopefully we can build on that next year and in the coming years.
"I think Sam knows he needs three or four players that can improve [the squad]. There are places where we can improve and that's where he'll be looking this summer.
"It's a process now of building ourselves in the Premier League and improving every year.
"There's a real stability around the Club - I don't think Sam has ever struggled with his teams in the Premier League. He's done a good job and I'm looking forward to the next couple of years."
Devonshire, who played 448 games for the Club in the 1970s and 80s, is now manager of Braintree Town, who also enjoyed a successful 2012/13 campaign.
He explained: "We did great. We finished ninth in the Conference and we did the double over Luton and beat sides at our place when they were top of the league.
"A lot of credit goes to the players for a fantastic year, they've done ever so well.
"Realistically, Braintree's aim is staying in the league until we get a new ground. That's the ideal situation."