The 52-year-old believes Manchester City, Liverpool, Tottenham and Manchester United will occupy the spots when the season ends.
Despite admitting Liverpool are playing good football, the former Newcastle United player is optimistic Pep Guardiola’s side will defend the title, but Arsenal will finish with Europa League qualification, a status the Gunners enjoyed last term.
"Man City have got players to replace every position on the field. Tottenham don't. Mauricio Pochettino needs to buy again in the next window and get a couple of players in," Gascoigne told the Men.
"Liverpool are looking strong as well but I cannot see anyone stopping Man City. They are just going to keep on buying and it's quite scary.
"I think it will be Man City, Liverpool, Tottenham and Manchester United [in the top four]. I think Arsenal are playing good football as well."
Paul Gascoigne, during his playing days, represented clubs like Rangers, Lazio, Tottenham Hotspurs, among others before venturing into football management as he managed Conference North club Kettering Town in 2005.
Featuring 57 times for the England national team, Gascoigne scored 10 goals for the Three Lions as he was regarded as the most talented English player.