The Merseyside outfit have made an impressive start to the current Premier League campaign following five successive victories.
Liverpool FC passed their biggest of the Premier League season so far after the Reds edged to a 2-1 victory over Tottenham Hotspur at Wembley.
The 18-time English champions further underlined their development over the past few months with a huge Champions League triumph.
Liverpool FC were 3-2 winners against Paris Saint-Germain in their Champions League opener thanks to Roberto Firmino’s late winner.
The Reds haven’t won silverware since Jurgen Klopp took over the reins from Brendan Rodgers in October 2015.
Former Liverpool FC midfielder Ince believes the Reds will challenge for the Premier League title.
“You could sense the frustration and anger when they conceded two, but they still got that goal when they needed it most,” Ince told Paddy Power.
“Liverpool fans are right to be excited. There are a lot of positive signals coming out of the club at the minute.
“For the first time in a long time, people you speak to are fancying them to win the title.
“I can’t see anyone coming close to them and Man City to be honest.
“The signs look great for trophies, the best they’ve looked in years and fans should be feeling very hopeful.”
Liverpool FC finished in fourth spot in the Premier League table last term to secure a spot in the Champions League.
The Reds haven’t won the Premier League title but have finished in second place in 2002, 2009 and 2014.
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