The England captain also appeared to labour through the first few games of the new season, even though he scored two goals in four games.
It's a very controversial idea - especially when Liverpool reached the Champions League final last season experiencing some magical moments on the way to Kiev.
Last season's Champions League runners-up open their campaign at home to Paris Saint Germain on Tuesday and, though Klopp admits he must rotate with seven games to play in 22 days, it will not be to dismiss the competition that Liverpool won five times.
'Gary should come over and tell me exactly how that works.
"How do you prepare a game when you don't focus on it?" You bring your kids in the Champions League? That would be amusing.
'I don't want to be too critical as I don't know exactly what or why he said it, but it's a bit silly, sitting in an office talking about football, it's different to doing the job'.
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Despite their European run last in 2017/18, Neville believes that the Reds are going to have to put the Champions League to one side, if they are going to win their first league title for over 25 years.
"He comes from another league, a completely different system which Monaco played, and we have a good team together so that takes time".
Pochettino said: "Look, when in England the transfer window closed and in Europe closed I think we move on".
"If it's late in the season that you see you have a chance to do that or do this and all that stuff".
"With a star-studded side full of attacking options the Reds are nearly always guaranteed to score and will look to heap more misery on the hosts who were beaten at Watford last time out".
Klopp welcomed back the last of Liverpool's worldwide contingent when Alisson Becker, Fabinho and Roberto Firmino returned to training on Thursday.