Joe Cole has said West Ham qualifying for next season's Champions League would be one of the biggest accomplishments in the club's history.
The Hammers put on a spirited performance despite falling to a 2-1 defeat to runaway leaders Manchester City, in Saturday's early kick-off.
West Ham could slip out of the top-four by the end of the weekend, should Chelsea beat Manchester United on Sunday.
But Cole praised West Ham's performance and said it would be a huge achievement for the club to achieve a top-four finish.
He told BT Sport after the game: 'You get into the top-four this year and it's one of the biggest achievement in the club's history.
'If you keep going in the right direction and into the upper echelons of the league regularly, you'll attract players because you're London and it's a great club.
'It's exciting times. I'd love to see a Barcelona or an AC Milan coming to the London Stadium because the fans deserve it.'
Manchester City took the three points with goals from Ruben Dias and John Stones, while Michail Antonio scored for the Hammers.
The Hammers came close on several occasions to score again but they were unable to find an equaliser.
Cole added: 'If West Ham had come away from this with a 2-2 City couldn't have complained, and that's credit to West Ham.
Should West Ham finish in the top-four, it would mark their highest league finish since third in the 1985-86 season.
West Ham with 45 points, already have more than the 39 they achieved as they finished 16th in the Premier League standings last season.
They currently sit two points ahead of London rivals Chelsea, and five ahead of Merseyside clubs Liverpool and Everton, all who have at least a game in hand.