The Reds moved to within six points of fourth-placed Manchester City thanks to their 3-0 victory over Manuel Pellegrini’s side at Anfield on Wednesday night.
Adam Lallana and James Milner scored first-half goals to put Jurgen Klopp’s side in charge before Roberto Firmino sealed an emphatic win as the Reds exacted revenge on the Eastlands outfit.
Liverpool make the trip to Crystal Palace in the Premier League at Selhurst Park on Sunday afternoon as Klopp’s side look to secure three successive top-flight wins.
Speaking on the Alan Brazil Up Front podcast, former Arsenal playmaker Parlour insisted that Liverpool are still contenders for a top-four finish.
“Liverpool will be looking at the top four,” Parlour said.
“They’ve got a game in hand on Manchester United. If they win it, they’re points behind Manchester United.
“They’ve got some big games but Jurgen Klopp will be demanding [more].”
Liverpool host bitter rivals Manchester United in the first leg of their Europa League last-16 clash at Anfield next Thursday.
The Reds lost to City on penalties in the League Cup final at Wembley last weekend.
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