The Gunners were one of the busiest clubs in the top half of the Premier League in the summer transfer window as Unai Emery moved to bolster his squad ahead of his second campaign in charge.
Arsenal signed William Saliba before loaning him back to Saint-Etienne, and also completed permanent deals for Gabriel Martinelli, Kieran Tierney, David Luiz and Nicolas Pepe.
The north London side also landed Dani Ceballos on loan from Real Madrid for the season, and the Spaniard has already impressed in an Arsenal shirt.
Attentions will gradually start to turn towards the January transfer window in the coming weeks and months as Premier League clubs consider bolstering their squads in the new year.
And former England striker Phillips believes that there are two key areas that need bolstering in the Arsenal side.
Speaking in an interview quoted by the Daily Express, Phillips said: “I’m talking about finishing in a Champions League spot where they haven’t been for quite a while now,” Phillips said on The Debate.
“I think so [top four would be a success] yeah, progression.
“If they can get to January they might add again. If what we’re hearing’s true there’s going to be money available.
“Go and get that defensive midfielder, go and get another powerhouse centre-half, really make yourself strong challengers.
“In terms of the title, I don’t see anyone challenging City or Liverpool for a bit.
“But I think progression for Arsenal, to get into the Champions League is the main priority this year.
“I think get to January, if they can add to the squad and are sitting in a healthy position, then they might have a chance yeah.”
Arsenal have not won the Premier League title since their famous unbeaten triumph in the 2003-04 campaign.
The Gunners will take on Liverpool FC in the Premier League at Anfield on Saturday afternoon.
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