The midfielder believes Arsenal need to improve up front, in midfield and potentially even defence.
The Gunners have been quiet so far, with their only deal of the summer being the capture of Petr Cech from Chelsea.
That move has been considered a coup for Arsene Wenger, with it being believed that Cech has seriously improved one of the weaker areas of his team and fixing one of the biggest problems they have faced for some time.
Arsenal's season got off to a disappointing start last week though as they were comfortably beaten 2-0 by West Ham at home, and Savage says they may have to improve in another three areas.
“Looking at the frustration written all over Arsene Wenger’s face, I have my doubts about other areas of his team,” he wrote in his Mirror column.
“Francis Coquelin has come on in leaps and bounds but he’s no Patrick Vieira. Olivier Giroud has scored 41 goals in 82 Premier League starts, but I still think Arsenal need a world-class centre forward. And if they continue to leak goals from set-pieces they may need another centre-back, too.”
Defensive midfield recruits needed
Of the three areas mentioned, it is arguably the defensive midfield position which is of the most concern to Gunners fans.
Coquelin has been a sensation since coming into the side, but beyond him there is very little cover, and should he pick up an injury, there is nobody to replace him.
Given that Wenger has a number of forwards to choose from then, perhaps he will target further additions in this area to bolster his squad instead, despite the consistent rumours of a move for Karim Benzema.