The Reds were 2-1 winners against Fulham at Craven Cottage in their final Premier League game before the international break.
James Milner scored from the penalty spot in the 82nd minute after Ryan Babel had cancelled out Sadio Mane’s opener.
Liverpool FC hoisted themselves above Manchester City and two points clear of the defending champions at the top.
Manchester City can restore their lead when they welcome Fulham on Saturday 30 March before the Merseyside outfit take on Tottenham a day later.
The Citizens won’t have the chance to make up their game in hand until the title holders take on Manchester United at Old Trafford on Wednesday 24 April.
Former England defender Neville believes the Premier League fixture schedule has provided Liverpool FC with a chance to take the initiative in the title race.
“They’ll have known that was a big moment. There will be times where Liverpool drop points before the end of the season, so too will Manchester City I think, but it couldn’t be against Fulham,” Neville told Sky Sports.
“Manchester City’s game in hand is at Manchester United, at Old Trafford, on April 24.
“There’s an opportunity for Liverpool here to step clear, with City not catching up for a few weeks, with the added complication of an FA Cup semi-final too. It’s a good thing for Liverpool, I believe.”
Liverpool FC are looking to win their first Premier League title and their maiden trophy under Jurgen Klopp.
The Reds will take on Portuguese club FC Porto in the Champions League quarter-final in April.
The Merseyside outfit were 5-0 aggregate winners against FC Porto in the Champions League round of 16 last term.
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