Gunners boss Unai Emery has suggested that the club are close to completing three or four signings in the coming days.
The Europa League side have added just one player this summer, 18-year-old Gabriel Martinelli, while they have witnessed a handful of first team stars exit on free contracts, including Aaron Ramsey.
Emery has been hamstrung by a small budget following the club's failure to qualify for the Champions League.
Arsenal have been linked to a host of players and have had bids rejected by Celtic for Kieran Tierney, which has left fans of the Premier League side frustrated.
However, Emery sought to allay concerns over transfers while speaking in Los Angeles during the club's pre-season tour.
He said: "Our target is to get three or four players who really improve our squad now. We are being very, very demanding and first speaking about the possibility to sign very expensive players. The first player in our list is our first target, if we cannot achieve that the second.
"We are waiting for two, three, four players to help us and also with everybody creating a new way with a lot of positive things we worked on last year. We need to take the best players in some positions, really being demanding of ourselves for these players.
"Really I can say to our supporters we are going to make a very good team with the players there now and three or four players who can help us in a few days."
Celtic are sticking to their £25million valuation of Tierney with boss Neil Lennon noting the £50million fee Manchester United paid for the far less experienced Aaron Wan-Bissaka.