The Merseyside outfit won their opening five Premier League fixtures to keep pace with current leaders Chelsea FC.
Liverpool FC eased to victories over West Ham, Brighton, Leicester City and Crystal Palace in their opening four games.
The Reds passed their sternest test of the Premier League season with a 2-1 win against Tottenham Hotspur at Wembley earlier this month.
Liverpool FC edged to a 3-2 win against Paris Saint-Germain in their Champions League opener at Anfield on Tuesday night before a 3-0 victory over Southampton on Saturday.
Former Arsenal star Keown believes Liverpool FC’s title rivals will be worried about Jurgen Klopp’s side after their strong start.
“Liverpool’s main man may not be firing on all cylinders but his team-mates seem to have raised their game by an extra 10 per cent to compensate,” Keown told the Daily Mail.
“The fact they have still won their first six games of the season will strike fear into their rivals.
Liverpool FC are looking to win the Premier League title for the first time after the Reds won the English top flight back in 1990.
The Merseyside outfit signed Fabinho, Naby Keita, Alisson Becker and Xherdan Shaqiri in the 2018 summer transfer window.
Liverpool FC haven’t won the Champions League title since 2005 when the Reds beat AC Milan on penalties.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news