The Reds were held to a 1-1 draw away to City at the Etihad Stadium on Sunday, meaning they go into the November international break in third place in the Premier League.
Despite their 7-2 hammering at the hands of Aston Villa earlier this season and suffering injuries to Virgil van Dijk and Fabinho, Jurgen Klopp’s side have still been able to churn out results.
Their title rivals City are in 10th place after winning just three of their opening seven league games.
Meanwhile, United and Arsenal have struggled for form this season and are both in the bottom half of the table.
And Deeney is expecting Liverpool to retain their crown, with City in second place, and in-form Spurs and Chelsea to battle it out for third.
‘I think the top four, personally, will have Spurs, Liverpool, Chelsea and City, not in that order,’ Deeney told talkSPORT.
‘I still think Liverpool will win it; City second and then it’s a toss-up between Spurs and Chelsea.’
‘We are always hungry for more but we have to be happy,’ he told the club’s official website.
‘I think when we started getting some injuries and lost a couple of players with Covid-19, everyone expected the wheels to fall off.
‘In the Premier League we’ve maybe not been at our best at times but we’ve picked up results and that’s why we are near the top of the league.
‘So, long may that continue and long may we keep building our confidence and building our performances.
‘I think this was one of our best performances in a while and hopefully we come back from internationals full of confidence and we can really kick on because we are a good team.
‘I hope we go and attack this Christmas period because it’s going to be hectic, but we have dealt with it pretty well in previous seasons and that’s what we need this season.’