Chelsea is currently at the fourth place in the Premier League standings with 63 points from 37 matches.
The German apologised for his conduct after the game and said that he should have dealt with the situation differently.
Klopp is understood to be open to the idea of a move, the reports said, adding that talks between Liverpool and his representatives were progressing well.
'If you were to lift the two trophies, I think you have a pretty good chance to be on a nice list of captains that have achieved great things in this club.'
Liverpool manager Jurgen Klopp could enter the transfer market after Philippe Coutinho and Dejan Lovren suffered hamstring pulls to deepen the club's injury crisis, British media reported.
Liverpool's wide range of goalscorers this season is a direct result of their attacking style, according to manager Juergen Klopp.
Former Manchester United manager Alex Ferguson said he was worried about the impact manager Juergen Klopp was having at his old team's great rivals Liverpool.
Manchester United manager Jose Mourinho played down the touchline confrontation that flared up between him and Liverpool manager Juergen Klopp near the end of Sunday's Premier League draw.
Juergen Klopp's reign as Liverpool manager began with a few points made but only one gained from an exciting, end-to-end 0-0 draw against Tottenham Hotspur at White Hart Lane on Saturday.
Liverpool's Juergen Klopp has been named Premier League manager of the month after leading the club to three consecutive wins in September, the first time the German has won the award.
Liverpool have put 2016's 3-1 defeat by Sevilla in Basel well behind them and are firing on all cylinders in Europe's elite club competition in this campaign.
Klopp said he was not surprised by the levels which his team continue to produce during a Premier League season in which they have yet to lose.
Free from the extra burden of European football, Liverpool have a strong chance to win the Premier League this season under a "ruthless" Juergen Klopp, according to Bayern Munich striker Robert Lewandowski. Liverpool, who finished eighth in the league standings last season, are fourth in the table this campaign, having beaten Arsenal, Chelsea and champions Leicester City in their opening seven games.
Liverpool's new manager Juergen Klopp promised to bring 'full throttle' football with a 'big heart' to Anfield in his first comments since the German was unveiled as the Merseyside's club new manager on Thursday night.
Liverpool are determined to end the trend of selling their best players during the close season in order to build a squad capable of consistently challenging for major honours, manager Juergen Klopp said.
Juergen Klopp's Europa League nightmare came true on Friday when his Liverpool side was drawn to meet former club Borussia Dortmund in next month's quarter-finals.
Juergen Klopp returns to the scene of one his Liverpool side's most controversial victories of last season this Saturday with the man who fashioned it lining up against him.
Jose Mourinho and Juergen Klopp's conflicting views on Neymar's imminent move from Barcelona to Paris St Germain offer an insight into how the 222 million euro (199 million pounds) deal has divided opinion across football.
Juergen Klopp refused to rule out Liverpool as Premier League title contenders on Wednesday after ending the year level on points with Manchester United and nine behind leaders Arsenal.
"...This club is built on what they did. It's built ... on (Bill) Shankly, (Bob) Paisley and (Joe) Fagan and all the others, but on these players... Steven Gerrard -- this club's built on, in the last 20 years, on Stevie's legs..."
'He went for a big hug and I just fell into his arms, looking exhausted' 'It means a lot as a player if your manager is genuinely showing some affection to you'
'It was a great atmosphere, I am so pleased for all of the people who have had harder times with us this season'
Liverpool manager Juergen Klopp called for his players to "stay calm" and does not expect to expect wholesale changes against Burton Albion on Tuesday as they seek to quickly bounce back from their 2-0 defeat at Burnley.
Liverpool players hail Juergen Klopp impact after defeating City.
After a six-match unbeaten start to his reign as Liverpool manager Juergen Klopp came down to earth with a bump as his side lost 2-1 to Crystal Palace in the Premier League on Sunday.
Former Manchester United manager Alex Ferguson will reportedly be consulted over the appointment of the successor of the sacked David Moyes at the Old Trafford club.
Liverpool has displayed a good performance so far in both Premier League and Champions League this season.
Manchester City will return to action in the UEFA Champions League on Wednesday against RB Leipzig at the Etihad Stadium.
Borussia Dortmund relish their status as underdogs for the Champions League final and are determined to prove they belong among Europe's elite, coach Jurgen Klopp said after they knocked out Real Madrid on Tuesday.
Juergen Klopp could not find a more fitting club to take his successful coaching career to the next level. Take a look why...
Mamadou Sakho faces an uncertain future at Liverpool after the defender was sent back to England from the Premier League club's pre-season tour of America. According to British media reports, manager Jurgen Klopp was unhappy with the 26-year-old's attitude during their stay in California and ordered his return to Liverpool.
There is often nothing more dangerous than a striker with a point to prove as Daniel Sturridge and Divock Origi showed in Liverpool's League Cup mauling of Southampton on Wednesday.
Man United get injury boost ahead of Liverpool FA Cup clash
Liverpool manager Juergen Klopp said elite-level coaches cannot give guarantees about their touchline behaviour due to the pressure that comes with being involved in the Premier League but he urged his counterparts to set higher standards.
Mario Balotelli has revealed that joining the Anfield club was the worst decision he has ever made.
Goals rained in for Manchester City and Manchester United but Juergen Klopp's first game as Liverpool manager was solid rather than spectacular as they drew 0-0 at Tottenham Hotspur in the Premier League.
Liverpool added on their website that the furloughed staff would continue to receive 100% of their salaries. Several English top-flight clubs, such as Tottenham Hotspur, Bournemouth and Newcastle United, have already put non-playing staff on furlough, with football's return in England contingent on medical guidance and government support.
Liverpool manager Juergen Klopp is a fan of Leicester's playing style.
Former Liverpool manager Brendan Rodgers believes lack of European football will be an advantage for the club in the Premier League and same will be the case for Chelsea.
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