Media reports said former England manager Roy Hodgson was in line to replace De Boer at Selhurst Park.
Last term, stung by City's woeful performance the previous season in a 3-0 Champions League loss at Anfield, Guardiola adopted a cautious approach in a goalless draw.
Fabinho's first-half goal earned Liverpool a 1-0 win at Burnley
IMAGES from the EPL matches played on Saturday
Chelsea moved into the Premier League's top four as Mason Mount's superb first-half goal earned them a 1-0 win at champions Liverpool who suffered a club-record fifth straight home league defeat on Thursday.
But after English FA's intervention, the Bundesliga giants have now allowed the 17-year-old to feature in Steve Cooper's side only for the group stages.
Lucas ended a goal drought stretching back to 2010 and Divock Origi missed a late penalty as Liverpool beat fourth tier Plymouth Argyle 1-0 in an FA Cup third-round replay on Wednesday.
Juergen Klopp's side, chasing their maiden title in the Premier League era and first in the top flight in 30 years, took a 14th-minute lead from a Virgil van Dijk header but had to wait until stoppage time to put the game to bed through Mohamed Salah.
Aymeric Laporte's late header sealed a deserved 1-0 victory over Tottenham Hotspur
IMAGES from EPL matches played on Sunday.
Champions Liverpool suffered a shock 1-0 defeat to lowly Burnley on Thursday, ending their 68 match unbeaten home record in the Premier League as their title defence continued to fade.
Winter returned to Anfield on Friday but while the temperature dropped, the standards of Juergen Klopp's side certainly did not as Sadio Mane and Mohamed Salah both struck twice in a 5-0 thrashing of relegated Huddersfield Town.
Liverpool regained their place at the top of the English Premier League with a 2-0 win at Cardiff City on Sunday that restored their two-point lead over Manchester City
The reigning champions have won 53 and drawn 11 of those 64 games, scoring 169 goals and conceding 42 for a total of 170 points.
Manchester City came from behind twice to earn a 2-2 draw with Liverpool in a breathless and pulsating Premier League encounter, at Anfield, on Sunday. All four goals came in the second half.
Manchester City now need, at most, 11 points from their remaining seven matches to secure their third Premier League title in four seasons.
Goalkeeper Alisson Becker scored a stunning header in the fifth minute of stoppage-time as Liverpool snatched a 2-1 victory at the death against relegated West Bromwich Albion at The Hawthorns on Sunday.
An extra-time goal from Roberto Firmino gave Liverpool a 1-0 victory over Brazil's Flamengo to win the Club World Cup at the Khalifa International stadium on Saturday. It is the first time Liverpool have won the competition, which features each continent's champions, and they became only the second English team to lift the trophy after Manchester United in 2008.
Roberto Firmino struck a stoppage-time winner as Liverpool beat Paris St Germain 3-2 at Anfield on Tuesday after Kylian Mbappe looked to have secured a point for the French side in a compelling Champions League Group C clash.
Liverpool opened up an eight-point lead at the top of the Premier League with an emphatic and hugely impressive 3-1 win over defending champions Manchester City.
A round-up of Saturday's matches in the English Premier League.
Images from EPL matches played on Wednesday
Tottenham Hotspur and Liverpool raised the spirits with a rip-roaring 2-2 draw in a pre-Christmas Premier League classic on Sunday after a weekend marred by COVID-19 related postponements.
England manager Gareth Southgate may be recovering from a dislocated shoulder suffered while jogging, but he may run into more discomfort when deciding whether to drop Raheem Sterling for Marcus Rashford in Sunday's World Cup game against Panama.
The following are talking points from the weekend's Premier League action:
IMAGES from the EPL matches played on Wednesday
Premier League champions Liverpool maintained their 100 per cent start to the season with a 3-1 win against Arsenal at Anfield on Monday leaving them level on nine points with pacesetters Everton and Leicester City.
News of all that's transpired on and off the football field
European champions Liverpool made an emphatic start to the new Premier League season by scoring three times in the opening half an hour as they taught promoted Norwich City a harsh lesson with a 4-1 thrashing at Anfield on Friday.
Leroy Sane struck the winner as Manchester City beat Liverpool 2-1 in a gripping English Premier League clash.
Liverpool ripped apart Manchester City with three goals inside the opening 31 minutes as they won their Champions League quarter-final, first leg tie 3-0 on Wednesday.
News of all that tranpired on and off the football field.
IMAGES from the English Premier League match played between Manchester United and Liverpool at Old Trafford on Saturday
Images from the English Premier League matches played on Saturday.
IMAGES from Premier League matches played on Sunday.
A round-up of Tuesday's action in the UEFA Champions League.
Liverpool manager Juergen Klopp has a midfield conundrum and his Tottenham counterpart Mauricio Pochettino must decide whether Harry Kane is ready for action as both bosses face selection dilemmas for Saturday's Champions League final.
It was not so much the maths, though Liverpool's nine-point advantage over defending champions City, with one point less over Leicester City and Chelsea, is a significant gap, especially as Juergen Klopp's side have lost one league game in 18 months.
Salah back in Liverpool squad but may not be risked at Genk, says Klopp
IMAGES from the English Premier League matches played on Saturday