The Hammers are in fifth place and three points behind third-placed Arsenal after their 3-2 victory over Everton in their last Premier League game.
Liverpool are in eighth place in the table but Jurgen Klopp’s side can move to within four points of Manuel Pellegrini’s City side if the Reds win their game in hand.
Slaven Bilic’s Hammers side, who drew 1-1 with Manchester United in the FA Cup last eight last weekend, have won their last three games in all competitions.
Liverpool have only lost three times in their last 15 games in all competitions.
Speaking to BT Sport, former Reds striker Owen talked up Liverpool and West Ham in the race to secure a top-four finish.
“It isn’t outrageous at all,” Owen said.
“A few weeks ago, the top four looked set in stone.
“I don’t think the top four will be the same as it is now. There will be a surprise.”
Liverpool set up a Europa League quarter-final clash against Borussia Dortmund after a 3-1 aggregate win against United.
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