Rabiot is off contract at the end of this season.
ESPN says the Reds have enquired about the availability of Rabiot.
In an interview with RMC last year he said: "I would love to play in the Premier League.
"I was very fond of Liverpool when I was young."
Klopp is a long-term admirer of Rabiot and even tried to sign him when he was manager of Borussia Dortmund.