The Merseyside outfit have made a brilliant start to the Premier League season following six successive victories to start the 2018-19 campaign.
Liverpool FC were 3-0 winners against Southampton at Anfield last weekend to hoist themselves to the top of the Premier League table.
The Reds eased to a 3-2 victory over Ligue 1 side Paris Saint-Germain in the Champions League group stage at Anfield on Tuesday night.
The 18-time English champions will make the difficult trip to Chelsea FC in their next Premier League fixture at Stamford Bridge next weekend.
Former Arsenal striker Hartson believes Liverpool FC are in contention to win the Premier League or the Champions League but won’t win an unprecedented quadruple.
“Liverpool can win a lot of games,” Hartson told BBC Radio 5 Live. “Can they win four trophies? I don’t think so.
“If you offered Klopp the league title or the Champions League, I think he would be delighted.”
Liverpool FC finished in fourth place in the Premier League table to continue to progress under Jurgen Klopp.
The Merseyside outfit will take on Serie A side Napoli in their second Champions League group stage fixture next month.
The Anfield outfit signed Fabinho, Naby Keita, Alisson Becker and Xherdan Shaqiri in the summer transfer window.
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