The Reds welcomed the Premier League leaders to Anfield in the first leg on Wednesday night looking to beat the Citizens for the second time this term.
Liverpool FC broke the deadlock in the twelfth minute after Mohamed Salah scored his 38th goal in all competitions in the current campaign.
England international Alex Oxlade-Chamberlain doubled the home side’s lead with a brilliant long-range strike to give Liverpool FC a commanding lead.
The Merseyside outfit polished off a commanding first-half performance with their third goal courtesy of Sadio Mane’s close-range header.
Manchester City were 5-0 winners against Liverpool FC at The Etihad back in September, although Sadio Mane’s sending off contributed to the result.
Former Leicester star Savage isn’t writing off Manchester City ahead of the second leg at The Etihad next week.
“I don’t think the tie is over,” Savage told BBC Radio 5 Live.
“3-0 to Liverpool. No Henderson. Is Salah going to be fit? I don’t think the tie is over – unbelievably.”
Liverpool FC signed Netherlands international Virgil van Dijk from Premier League rivals Southampton in the January transfer window.
The Reds haven’t won the Champions League since 2005 when Liverpool FC came from 3-0 down to beat AC Milan on penalties in Istanbul.
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