Arsenal manager Unai Emery insists the club are targeting "very big, very expensive" deals in the transfer market.
Arsenal have 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 Spaniard.
Sky Sports News understands the Gunners have had bids rejected for Crystal Palace winger Wilfried Zaha and Celtic left-back Kieran Tierney, and are understood to be in advanced talks to sign Saint-Etienne defender William Saliba and Real Madrid 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."
Arsenal director Josh Kroenke, son of owner Stan, responded to an open letter from fans criticising his father's running of the club on Monday.
Emery says he and recently-appointed technical director Edu are in close contact with the Kroenkes over the club's recruitment strategy.
"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."
Nicholas: It's a true concern
Speaking on the Transfer Talk Podcast, Sky Sports' pundit Charlie Nicholas has his concerns about Arsenal's transfer strategy this summer, and supports fans' recent calls for a restructure.
"I totally support the Arsenal fans' statement. The concern has been growing for 18 months, about the lack of atmosphere, lack of ambition. I think the criticism is fair.
"Now there's a situation whereby there are too many chiefs trying to have a say. Are there too many guys sitting on the committee? It's getting a bit out of control.
"If Arsenal are going after defenders, which they need more than anything else, then go and nail them down, go and make a statement of intent.
"Arsenal have to force the issue. I know times have changed, but Arsenal are finding it damned hard to compete at a big financial level. It doesn't seem as if there is a strategy, and that is a true concern."
Follow the Summer Transfer Window on Sky Sports
Sky Sports News is home to three new shows dedicated to bringing you the very latest news from this summer's transfer market.
Start your day with Good Morning Transfers at 9am as our team of reporters and pundits bring you the latest news and insight. Transfer Talk then follows at midday, delivering the biggest stories that matter to you. And join us at 7pm for the definitive round-up of the day's news with The Transfer Show.
And as well as tuning into Sky Sports News, don't miss a thing with our dedicated Transfer Centre blog.
There's also the Transfer Talk Podcast, the daily UK, Regional and European Paper Talk, plus features across skysports.com and the Sky Sports app.