Arsenal manager Unai Emery insists the club are targeting "very big, very expensive" deals in the transfer market.
Arsenal has only signed 18-year-old winger Gabriel Martinelli so far this summer but remain focused on bringing in another three or four players who can go straight into the first team, according to the manager.
The Gunners have had bids rejected for Crystal Palace winger Wilfried Zaha and Celtic left-back Kieran Tierney, and there have also been talks with Saint-Etienne's teenage central defender William Saliba and Real Madrid outcast central midfielder Dani Ceballos.
"Our target is to achieve three, four players to really improve our team and squad now," Emery said ahead of Arsenal's pre-season game against Bayern Munich.
"We are being very demanding and we are also first speaking about the possibility to sign very big players, very expensive.
"The first player in our list is the first target and after, if we cannot have that then [we try to sign] the second, but thinking every time that they are going to improve our team."
Emery says he and recently-appointed technical director Edu, an ex-Arsenal midfielder, are in close contact with the Kroenkes over the club's overall transfer policy and recruitment strategy as a whole.
"We are having a lot of meetings with the club, with [technical director] Edu, also with Josh and Stan Kroenke in Denver," Emery added.
"We have a very clear idea: to sign the players who can help us with a good performance and in the positions we need."
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