Liverpool are languishing in the Premier League table, and the Reds have rarely gone into a Merseyside derby under more pressure.
Dalglish has hardly enjoyed the best of starts, with Liverpool against old rivals Manchester United in the FA Cup last weekend and then going down to Premier League defeat against Blackpool in midweek.
Hardly the best of starts: Dalglish looks on as Liverpool slump to another defeat at Blackpool on Wednesday night
On Sunday he faces the true test of his worth - hosting the latest bitterly-contested clash with neighbours Everton.
It is a moment that could dictate the future of Dalglish and the struggling club - so to mark the occasion, Sportmail have picked out five classic Merseyside derbies from Kenny's previous reign as manager at Anfield.
Everton 2-3 Liverpool, First Division, August 1985Dalglish, who had just been made player-manager, netted a beautiful opener from outside the area after only 20 seconds. New signing Steve McMahon added a second and Ian Rush, Liverpool's top goalscorer, beat Neville Southall to score their third before half time.
The second half was a very different affair, with a goal apiece from Everton's Graeme Sharp and Gary Lineker leaving the Anfield fans breathing a sigh of relief at the final whistle.
Liverpool 3-1 Everton, FA Cup final, May 1986Dalglish started the first-ever all-Merseyside FA Cup final in the No 7 shirt ahead of an injured Paul Walsh, seven days after Liverpool had pipped Everton to the league title.
Gary Lineker gave Everton the lead from Peter's Reid's 40-yard pass at Wembley, but Dalglish's men fought back after the break.
WATCH THE GOALS FROM THE 1986 FA CUP FINAL
Ian Rush equalised on 56 minutes, Craig Johnston put Liverpool in front five minutes later and Rush then scored again to seal the double.
Liverpool had won the fabled Double for the first time.
Memories are made of this: Kenny Dalglish celebrates with Bruce Grobbelaar after Liverpool's 1986 FA Cup final victory at Wembley
Everton 1-0 Liverpool, First Division, February 1988This was one of only two league defeats for Dalglish's squad in the 1987-88 season, with Everton bringing their 29-game unbeaten run to an end through a goal from Wayne Clarke.
The match came just six months after Everton chairman Sir Philip Carter condemned fans who had directed racist chants at Liverpool's John Barnes. Despite the loss at Goodison Park, Dalglish went on to take the title, with a squad many fans consider to be Liverpool's finest.
Liverpool 3-2 Everton (aet), FA Cup final 1989The second all-Merseyside FA Cup final came just five weeks after the Hillsborough disaster, with the players wearing black armbands, a minute's silence before kick-off and an emotional mass rendition of You'll Never Walk Alone led by Gerry Marsden of Gerry and the Pacemakers.
Dalglish's team claimed a dramatic win, with Stuart McCall twice equalising for Everton after goals from John Aldridge and Ian Rush - before the latter scored the winner for the Reds in extra time.
WATCH THE GOALS FROM THE 1989 FA CUP FINAL
Everton 4 Liverpool 4 (aet), FA Cup fifth-round replay, February 1991A drained Dalglish resigned the morning after this outstanding match at Goodison Park.
The rare start he gave Peter Beardsley paid off, as the Liverpool player scored twice. Ian Rush, inevitably, also netted for the Reds, but a determined Everton equalised repeatedly, thanks to two from Graeme Sharp and one from Tony Cottee with three minutes remaining. John Barnes struck a superb curler in extra time, but Cottee gave managed a fourth equaliser. Everton won the replay.
Dalglish departed, and it would be 20 years before his return.
The beginning of the end: Dalglish couldn't hide his disappointment after the 4-4 draw
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Explore more:People: Paul Walsh, Ian Rush, Steve McMahon, Neville Southall, Kenny Dalglish, Gary Lineker, Stuart McCall, John Barnes Places: Liverpool