The Reds are seven points clear of the defending champions, thanks in part to City suffering three defeats in their last five Premier League games.
Pep Guardiola's men have slipped back down to third ahead of the game courtesy of Tottenham's win over Cardiff City.
City led the table from the fifth game of the 2017-18 campaign on their way to claiming the title, accumulating 100 points and over a century of goals.
And due to enjoying such comfort, Barnes believes the champions are not used to the pressure which often accompanies a title race.
“Last year, they didn’t have to play with pressure," said Barnes, speaking exclusively for bookmaker comparison platform BonusCodeBets.co.uk.
"I always felt that this Manchester City team are the best team, possibly in the world and certainly in the country when everything is going well.
"When they’re 10 points clear, they play with freedom. Put them under pressure and we don’t know how they’re going to perform.
“All of a sudden Liverpool are a few points ahead of them and now they have to perform.
"That is one thing I would throw against them, the character that they have when things aren’t going well.”
“If they were 10 points clear ahead of Liverpool going there, I think they’d beat them, but with Liverpool being ahead, they are under pressure to perform and I don’t know whether they are going to be able to do that.
"I’d be surprised if Liverpool lost, put it that way.”
A 10th straight Premier League win for Liverpool would see them extend their lead over Spurs to nine points and take them 10 clear of City.
Tottenham's defeat to Wolves saw them lose ground earlier during the festive period but Barnes sees Mauricio Pochettino's side as the main opposition to denying the Merseysiders their first championship since 1990.
"Liverpool have not had a problem playing against Arsenal, Man United, Tottenham, Man City, the big teams.
"They’ve had a problem against the smaller teams, but since the Van Dijk signing, we look stronger and more capable of playing against the so-called lesser teams and winning.
"If Liverpool beat City, then when they play against the lesser teams, because of the confidence and intensity they’re playing with, they will confidently go on to win the league.”