Two years ago, Manchester City won the league at a canter, with Liverpool doing the same in 2019/20, but Walker expects the current campaign will be more competitive.
So far, both teams have dropped points in surprising circumstances and there have been shock results across the division, which has led many to brand this Premier League season one of the most unpredictable to date.
The right-back agrees, but hopes City will have the opportunity to build the sort of momentum our previous title triumphs have been built upon.
“Personally, I believe that no one is going to run away with it this season,” said Walker.
“I think there are going to be a lot of ups and downs, twists and turns in the story of the Premier League, but we just need to do our jobs.
“I feel as a team and as a club, if we perform and sing from the same hymn sheet, we can beat anyone in the world.
“If we just get a few good wins together like in the past, hopefully we can hit the ground running and keep going from there.”
City go into Saturday’s game at Sheffield United 13th in the table, with two wins from our opening five games.
Walker admits it is not an ideal situation, but overall, he has been satisfied with our start to the campaign.
“We have dropped some points that we shouldn't have dropped, especially the game against Leicester City with the defeat we suffered at home,” he added.
“But I think apart from that, we have actually done relatively well. Going to Elland Road against Leeds United was always going to be difficult.
“The first game of the season at Wolves was always going to be a tough one there because they are a good team, so I think we have picked up some good points in good areas, but the game against Leicester City probably does stand out to us.
"That can't happen again and we don't expect that as a team.”
It was Sheffield United who gave Walker his start in professional football and he returns to Bramall Lane on Saturday on the verge of his 100th Premier League appearance for City.
It is a landmark moment for the 30-year-old, who has been one of the stalwarts of our success under Pep Guardiola and something he is particularly proud of, given the competition he has faced at right-back.
“It's massive for me,” said Walker.
“From when I first signed here, there was me and Danilo, then Joao Cancelo came, so I have always had competition.
“To rack up the amount of games that I have done in such a short space of time is probably credit to myself, but I still feel great.
"I feel fresh, hungry, I'm so hungry to win more especially with this club and with this team because I feel that we work so hard.
“People don't see what we do off the field to try and make sure that when game day comes, we are ready, we know what to do in our roles and responsibilities for this team.
“To make 100 Premier League appearances is fantastic in any club but at Manchester City it's a really special achievement.”