The Hammers are only six points away from the top four in the Premier League, and their next two matches are against relegation threatened Aston Villa and Sunderland.
Nicholas feels that West Ham have a chance of making it into the Champions League spots this season, but he does believe they need to improve against struggling teams.
“Of course they have [got a chance of making it into the top four],” Nicholas said. “The thing is with West Ham is that they want to play against the big teams. That gives them a golden opportunity.
“The teams they are better than, they can let themselves down against.
“They had the opportunity two or three weeks ago to close the gap on Spurs, but at Newcastle away they didn’t turn up for 45 minutes.
“They are more than capable of getting to the top four. They are saying to take their time because of their new stadium, but this time is right.”
West Ham have generally been more impressive when allowed to play on the counter this season, and they have picked up some memorable results.
The Hammers have done the double over Liverpool this season, while they have also beaten Manchester City, Arsenal and Chelsea.
That good form has pushed them up to sixth in the standings, but they have also suffered damaging defeats against the likes of struggling Bournemouth and Newcastle United, while they also could only manage a draw with bottom of the table Aston Villa.
The Hammers have a chance to show that they can perform when they are the favourites later this evening, when they host Villa looking to pick up their first win in four matches.