Benteke limped off with a hamstring injury during the Reds' 1-1 draw with Norwich City last month and has been sidelined since.
The Belgium international, who signed for £32.5 million from Aston Villa in the summer, has scored two goals for Liverpool this season and was expected to play a pivotal role at Anfield.
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However, the 24-year-old is losing his battle against the clock to face Tottenham at White Hart Lane this weekend. Benteke scored the only goal in Villa's 1-0 victory away against Spurs last campaign.
The former Genk man's absence from Klopp's first game in charge could see him fall even further in the Liverpool pecking order.
With Klopp set to enforce his intense, counter-attacking football at Anfield, encouraged through a vast amount of work-rate, some are already predicting that Benteke might not suit the system.
He was dragged off at half-time during Belgium's 1-0 win against Cyprus last month, with manager Marc Wilmots criticising the striker's "half performance."
Klopp will not be short of options, though. Danny Ings has been highly praised by Liverpool fans since he joined Anfield in the summer - the ex-Burnley forward's performances have been selfless and his work-rate has been appreciated by many.
He has also proved he has an eye for goal, scoring three times in eight matches.
Klopp will be well aware of the talented Roberto Firmino and will have been delighted to witness the Brazil international return to full training on Wednesday.
Firmino was forced off midway through Liverpool's Capital One Cup victory against Carlisle United in September when he fell awkwardly, with scans showing he cracked a bone in his back.
The 23-year-old joined the Reds from Bundesliga outfit Hoffenheim for £29 million in July, with club chief executive Ian Ayre flying out to Chile to wrap up the deal whilst Firmino was at the Copa America with Brazil.
Klopp came up against Firmino on numerous occasions whilst manager of Borussia Dortmund and reportedly flirted the idea of signing the playmaker in 2014.
Firmino was given limited opportunities under Brendan Rodgers, who was sacked following Liverpool's 1-1 draw against Merseyside rivals Everton earlier this month following a string of poor results.
However, the attacking midfielder could feature much more under Klopp.
The 48-year-old might have opted for an easier fixture in his first game in charge of the Reds, though, if he could have hand-picked his opponent.
Spurs are rivalling Liverpool for a place in the top four this season and have lost just one match so far.
They put Manchester City to the sword in their last home game, thrashing Manuel Pellegrini's men 4-1, with the north London side gelling as a unit under Mauricio Pochettino.
Liverpool's positive record at White Hart Lane does offer Klopp plenty of optimism, however.
Two seasons ago, a Luis Suarez double inspired the Reds to a 5-0 victory and last term Steven Gerrard bagged a second half penalty to help Liverpool win 3-0.