Gerrard was hired as Villa boss last week after agreeing to leave Scottish champions Rangers.
Edwards has been a key figure in Liverpool's successful recruitment programme, but the 42-year-old is ending his 10-year association as he wants a fresh challenge.
Liverpool's habit of avoiding giving big contracts to players aged over 30 has fuelled fears Salah will leave Anfield.
The two head coaches have won the last four Premier League trophies, with City claiming three, and a fierce rivalry has developed between the clubs.
Standing at stadiums in English football's top two divisions has been banned since 1994 after the 1989 Hillsborough disaster, which led to the deaths of 97 Liverpool fans.
Just a week after Liverpool were forced to pull out of the controversial Super League following a furious public backlash, the reigning Premier League champions' revealed the financial impact of the coronavirus pandemic.
Premier League: Liverpool fans unfurl banners demanding removal of American owners ahead of Newcastle United game
“£nough is £nough FSG Out” and “Henry, You have blood on your hands,” were the words on some of the banners, referencing Fenway Sports Group and principal owner John Henry.
Sunday's 4-1 win over Liverpool at Anfield made it 14 victories in a row in all competitions for Manchester City, equalling the record for top-flight sides set by Preston and Arsenal.
Premier League: Liverpool bolster defence by signing Ozan Kabak, Ben Davies; Takumi Minamino off to Southampton
The January window is regarded as a sellers' market and often a time for stop-gap measures but Liverpool were forced to act.
Since the Premier League came into being, no club with fewer than eight points after 14 games have stayed up. This was West Brom's 14th game and they have seven points.
Champions League: Bayern Munich, Manchester City cruise to last 16; Liverpool slump to home defeat against Atalanta
On a night when clubs marked news of the death of Diego Maradona by holding a minute's silence in memory of the Argentine before all Champions League games, Bayern eased to a record-extending 15th straight win in the competition.
Premier League: Liverpool sign defender Kostas Tsimikas from Olympiakos for reported fee of £11.7 million
Kostas Tsimikas played 27 times in the league last season, winning the first major honour of his career as Olympiakos clinched the Greek title.
Premier League: Liverpool's Jurgen Klopp says Frank Lampard has lot to learn after Chelsea boss' jibe
Chelsea boss Frank Lampard was embroiled in a heated exchange with the Liverpool bench during their Premier League clash earlier this week.
Liverpool disappointed with fans not heeding to 'celebrate at home' advice; Merseyside police arrests 9
Visuals showed Liverpool fans flooding the streets outside Anfield, setting off fireworks, lighting flares and chanting together as Jurgen Klopp’s side beat Chelsea 5-3 in a thrilling encounter.
Premier League: Jurgen Klopp's Liverpool beat Chelsea in eight-goal thriller before long-awaited championship celebration
Liverpool ensured the end of their 30-year title drought long ago. Only the three-month delay to the season because of the coronavirus pandemic delayed the coronation.
Premier League: Jurgen Klopp advises fans to 'stay at home' to watch Liverpool lift trophy after Chelsea game
Having already clinched the title earlier with seven games to play, Liverpool will finally get to lift the trophy after their fixture against Chelsea at the Anfield.
Premier League: Liverpool to be presented with winner's trophy on iconic Kop stand after Chelsea game
Liverpool players have been involved in the planning of the ceremony, with club great Kenny Dalglish — the last manager to lead Liverpool to a league title — among the trophy presentation party.
Premier League: Jurgen Klopp's maddening levels of positivity the key to Liverpool's record-breaking success
Klopp is the biggest influence at Liverpool in the last three decades. He has transformed the club into a happy place and a desirable destination for players.
Premier League: Liverpool police to get tougher on crowds after wild celebrations amid pandemic worries
The move to stop gatherings of more than two people came after the sheer joy of Liverpool winning the Premier League title, together with warm weather, prompted people to cast off worries about the COVID-19 pandemic and to gather in huge crowds.
Being so revered sits uneasily with Jurgen Klopp when discussing legendary predecessors Paisley, Bill Shankly and Kenny Dalglish, who won the team’s last English championship in 1990.