Mauricio Pochettino's men booked their place in the Champions League last eight with a 1-1 draw against Barcelona at the Parc des Princes on Wednesday.
Mbappe plundered a stunning hat-trick to help his side to a 4-1 first-leg win at Camp Nou last month.
Kylian Mbappé, opened the scoring with a penalty against the run of play before Lionel Messi levelled with a superb long-range goal, but the Argentine had a spot-kick saved by Keylor Navas before the half-time.
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Jurgen Klopp’s side advanced to the quarter-finals of the Champions League.
Klopp praised Fabinho said, is "one of the best in the world at number six", after the Brazilian outstanding performance on Wednesday night.
The 27-year-old midfielder has had to fill in at centre-back for large parts of this season because of injuries to Virgil van Dijk and Joe Gomez, while also suffering from a number of fitness problems of his own.
Klopp said, "We have to see what solutions we can find for the next games but number six is his position.
"It was our hope to keep him there for the season. He is one of the best in the world in that position, that is clear - not only defending-wise but creating as well. He is so important to us."
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