The 2024-25 campaign will get underway on Friday night with Manchester United hosting Fulham, while Arsenal play their first game on Saturday when they will take on Wolves at the Emirates at 3pm.
In the last two seasons, Arteta's side have run Manchester City close in the race for the title, but have come out second best on both occasions, with City winning a record four titles in a row.
They will have high hopes of challenging again this year, however, with City losing some key players and Arsenal active in the market - and another year more experienced as challengers.
But they do need to win a trophy sooner rather than later, Shearer told The Rest Is Football podcast, to prevent pressure being placed on the Spaniard.
Alan Shearer has fired Mikel Arteta (pictured) a Premier League warning ahead of the new Premier League season
'It depends - if they don't win anything then you look at the bigger picture and how close they've come and how good their football is and their injury situation,' the Premier League's all-time leading goal scorer said. 'You have to look at all those things.
'But eventually he's going to have to win something, whether that is this season or not. But that has to come at some stage, doesn't it?
'We all recognise how formidable Manchester City are, there's no doubt about that, which makes it very difficult for Arsenal. But at some point he'll need to win something and take that extra step, but their progress has been really good.
Arteta has won just one trophy since taking over as manager of Arsenal in 2019 - the FA Cup in his first season in charge - and, though he has helped the club progress, there hasn't been much to show for it in terms of silverware.
Last season, his side finished two points behind City, taking the title race to the final day, while the year before they were five points short.
If they failed to win the league again, it will mark 21 seasons since they last lifted the Premier League.
City will play their first game of the new season on Sunday afternoon, taking on Chelsea at Stamford Bridge in Enzo Maresca's first game in charge of the Blues.
The Euro 2024 winner with Spain has become a top target for several big clubs, especially after his decisive goal in the European Championship quarter-final against Germany.
Real Sociedad are thought to be open to selling the player to avoid losing him as a free agent next year.