The Reds were in second place in the Premier League table ahead of their trip to Manchester City on Saturday evening.
Liverpool drew 3-3 with Watford in their top-flight opener after the Hornets scored a late equaliser at Vicarage Road.
However, the Merseyside outfit soon registered their first win of the 2017-18 season with a 1-0 victory over Crystal Palace.
Liverpool produced their best performance in a 4-0 victory over title rivals Arsenal in their last Premier League game.
Goals from Roberto Firmino, Sadio Mane, Mohamed Salah and Daniel Sturridge secured an emphatic win to underline their attacking prowess against a dismal Arsenal side.
Former Chelsea striker Sutton believes Liverpool are in good shape under former Borussia Dortmund coach Klopp.
“Liverpool are moving in the right direction. They’re brilliant to watch,” Sutton told BBC Radio 5 Live.
“They’ve got issues at the back. But Liverpool are on the up and full of positivity where Arsenal are embarrassing.”
10-man Liverpool lost to Manchester City on Saturday evening following goals from Sergio Aguero and Gabriel Jesus.
The Reds signed AS Roma winger Mohamed Salah, Chelsea teenager Dominic Solanke, Arsenal midfielder Alex Oxlade-Chamberlain and Hull City defender Andy Robertson this summer.
Liverpool agreed a club-record £48m deal to sign Naby Keita from RB Leipzig next summer.
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