The Hammers finished last season just five points above the relegation zone but head into Monday's game against bottom side Sheffield United firmly in the battle for the European places.

"If we can finish strongly great, but it will be very, very difficult with the teams challenging us and just below us," said Moyes.

"I think we are capable, but can we do it is another thing.

"I want to get West Ham involved with the big boys and if we are going to do that we have got to get into Europe.

"I don't know if we can do it this year and if we are ready, and it would be a humongous step we had taken if we even got close to that. It would be enormous.

"But if we are still in position when the games remaining comes down to single figures, let’s see if we can focus on one game at a time and see what we can do."

West Ham host Sheffield United on Monday

Moyes knows from experience that European football would mean a packed fixture schedule, but hopes that will be a welcome headache he has to deal with.

"The games come thick and fast," he said. "Prior to the game against Manchester United, the players and the staff had had no days off for about the full month since 3 January, so it’s been an incredible run just because of games.

"But in a strange way I hope in the future that’s the way it’s going to be and I’m going to talk about European games or something else because we’ve got game after game, and we’ll have to get used to that I hope.

"At the moment, the last month or two has been fruitful for us and it’s shown that we can cope with a game on a Saturday, Tuesday at this moment in time.

"What I would say is the Europa League has always been difficult with the Thursday/Sunday situation for any club. I remember the first year I was in it with Everton we were terrible and we got knocked out straight away.

"But once you get used to it and start to get a run in it – we lost to Fiorentina in the last 16 on penalty kicks one year (2008) – you get experience."