Klopp looks the front-runner, and is reporting he could be appointed by the end of this week, although Ancelotti was spotted in the UK over the weekend.
Both Klopp and Ancelotti are on sabbaticals and both could only be tempted back to full time work by the right offer, or the right project.
The World Game has run the rule over the two contenders, to find out what to expect from the new man in the Anfield hot seat.
Carlo Ancelotti
Who is he?
"Carletto" was a superb player in his own right, one who made more than 200 appearances for AS Roma and more than 150 for the legendary AC Milan side of the late 1980s.
As a manager, he has enjoyed a relatively nomadic career, starting with Reggiana, Parma and Juventus in his homeland, before an eight year spell at Milan. Spells at Chelsea, Paris St-Germain and Real Madrid followed before he decided to take a year off. Or will he?
Ancelotti is known to enjoy a joke and a crafty cigarette and was recently described by Alessandro Del Piero as
Why is he the perfect fit for Liverpool?
As a player and a coach, Ancelotti is a serial winner. He won Serie A three times, as well as the UEFA Champions League twice, in the only side to ever win European club football's holy grail back-to-back.
In the dugout, he has overseen, another two Champions Leagiue wins while at Milan, as well as another Serie A title. At Chelsea, Ancelotti won the Premier League/FA Cup double in his first season, and then he followed it up with Ligue 1 at PSG in 2013.
Finally, he brought Real Madrid "La Decima", its tenth UEFA Champions League title.
His teams play expansive, attacking football, the kind which nearly won Liverpool itself the Premier League in 2013-2014, and he is a likeable, affable character about who nobody has a bad word.
Why mightn't it work?
Liverpool need someone to not only pick up results now, but build for the future. It has won 18 First Division titles, but never has it finished top of the pile in the Premier League era.
They would dearly love a coach who can deliver sustained success and while Ancelotti is a man who almost guarantees trophies, he's not one who hangs around for the long haul.
His eight year spell was the longest of his managerial career and only two seasons at Chelsea, PSG and Real Madrid followed.
Chelsea and Madrid are two of the most volatile coaching positions in world football however, so Liverpool might fancy convincing Ancelotti Anfield is his forever home.
Jurgen Klopp
Who is he?
Klopp's playing career didn't have the razzle-dazzle of Ancelotti's, but he was a true one-club man, playing his entire career at Mainz 05.
The 193cm bean pole was a striker initially, but was converted to a defender half way through his career.
He made 337 league appearances, scoring 52 goals.
He'd not retired five minutes before he was appointed Mainz's head coach, where he spent seven years before moving to Borussia Dortmund, where he spent another seven seasons.
Klopp is energetic, charming and hugely popular with fans and players alike for his robust touchline celebrations and willingness to go into bat for his players.
Why is he the perfect fit for Liverpool?
Dortmund finished in the bottom half of the Bundesliga in 2007-2008, but Klopp's arrival heralded a transformation.
Sixth and fifth place finishes were followed by back-to-back Bundesliga titles, the latter of which included the Bundesliga's highest points total of all time, 87.
May 2012 also saw Dortmund complete a domestic double after it beat Bayern Munich in the DFB-Pokal Cup final.
A Champions League final in 2013, which was lost to Munich, was the peak of the Dortmund revolution.
Klopp proved he could harness the talents of Sven Bender, Marco Reus and Robert Lewandowski, while Nuri Sahin and Shinji Kagawa were both pivotal ingredients of Klopp's early success.
Klopp favours an aggressive, high intensity, pressing game which, when roared on by a fervent Kop, could prove formidable.
Why mightn't it work?
Klopp took two years to transform Dortmund before it became the Bundesliga powerhouse it was in 2010-2011 and 2011-2012, and there is an expectation of immediate success on Merseyside.
However, that expectation isn't necessarily realistic and with Klopp there should be more patience than there was with Rogers, whose side went backwards after the near-miss of 2013-2014.
Klopp's last season at Dortmund had echoes of Chelsea's current predicament. Lewandowski was sold to Munich and his replacement Ciro Immobile was exactly that, and scored only three goals in the Bundesliga.
Kagawa and Sahin returned but couldn't be restored to their former glory and for a while it looked as if a stunning relegation might be on the cards, after 11 losses in 19 games.
Dortmund finally clicked into gear in February, losing only three of its last 15 games to scramble to a seventh placed finish, but shorn of his top quality players, Klopp struggled to replicate his earlier success.
