The French international insists that "several players are questioning the club's future" and urged Arsene Wenger to sign proven match-winners to catch up Chelsea, Manchester United and Liverpool.
He said: "What is sure, it is that several players are questioning the club's future.
"Around us, all the teams are recruiting but what is planned to compensate for the departure of Titi Henry [to Barcelona]?
"I am not at Arsenal to play for third place. It is necessary to recruit players of reputation because the young players have many qualities but the season is very long.
"The young players are thirsty for victories but Arsenal must obtain results to gain titles. If not, one will have to change policy and do the same as the other teams: recruit with more means."
Gallas returns to pre-season training on Wednesday after spending his summer holidays in Guadeloupe with his family.
The defender said: "I will have a discussion with Arsene Wenger and board members to know the objectives of the club this season and what they wish to set up to build an even more competitive team."
Gallas had a difficult first season at Emirates Stadium after leaving Chelsea under a cloud. He joined as part of the deal that saw Ashley Cole leave for Chelsea.
Asked about his own future, he said: "Today I am at Arsenal but I do not know what can occur tomorrow.
"All happens so quickly in the world of football."
