Mikel Arteta’s side, who finished eighth in the English top-flight last term, have taken full points from their first two matches of the 2020-21 campaign and visit defending champions Liverpool on Monday.
Despite the encouraging signs from the Emirates, Souness has dismissed Arsenal’s title chances, while praising seven of Arteta’s players.
‘Arsenal are nowhere near challenging for the Premier League,’ Souness wrote in a column for The Times.
‘They finished eighth, 43 points behind Liverpool, last season, and that’s not a gap that you close in one transfer window.
‘The knockout tournaments are again their best chance of success this season. Trying to retain the FA Cup, a decent run in Europe and maybe the Carabao Cup.
‘I’ve always been a fan of Willian and have no fears that he still has a couple of years left at the highest.
‘The hardest players to get are the ones that score and create goals, but Arsenal have plenty of attacking options.
‘Willian, Alexandre Lacazette and Pierre-Emerick Aubameyang are backed up by talented youngsters like Bukayo Saka and Eddie Nketiah. Keeping Aubameyang is a huge boost.
‘I still see a player in Nicolas Pepe, too, and I’m hoping he has a big year because he’s not really grasped the intensity and physicality of the Premier League yet.
‘I also like the look of Bernd Leno, their goalkeeper, but none of their midfielders or back four would get anywhere near the Manchester City or Liverpool team, hence the points difference between them in the final table last season.’