The German boss replaced Brendan Rodgers last week and will take charge of his first game today when the Reds face Tottenham Hotspur.
His arrival has been greeted with incredible levels of excitement, but Neville does not understand why so much has been made of the 48-year-old's addition.
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Writing in his column for the Telegraph, the former England international said: 'I’m not sure whether Klopp reads our media, but I imagine he would be quite uncomfortable seeing the eulogies.
"There’s been quite a bit of fawning when he has yet to play a football match in England, never mind win one.
"It is almost as if Liverpool have to impress Jurgen Klopp. It should be the other way round. On the internet I came across ex-Liverpool players saying this was ‘a marriage made in heaven’ and ‘it’s giving me goosebumps.
"I bet Klopp can’t believe it. If a German manager went to Spain there is no way the Spanish would react in this manner. Here, it’s almost as if Liverpool Football Club feels blessed to have him - and I’m uncomfortable with that."
All the talk of Klopp's arrival has fuelled expectation on Merseyside, but now the time has come for the talking to stop and action on the field to take centre stage.
The trip to White Hart Lane gives the German the opportunity to become only the second Liverpool manager in Premier League history to win their first match.
Despite the Reds' recent history in north London, the game against Mauricio Pochettino's resurgent side will be no easy task.
Spurs are unbeaten since the opening day of the season and have won three of their last four matches, including a 4-1 demolition of Manchester City in their previous home fixture.
With Liverpool's squad being torn apart by injuries to six first-team regulars, the former Borussia Dortmund manager will have to make do with the players at his disposal.
While a victory in his first game as Anfield boss would be a dream start, taking a point away from today's match would be no mean feat.
Will Jurgen Klopp win his first game as Liverpool manager? Have your say by leaving a comment below!