Unai Emery insists Arsenal are working to bring in “three or four” players before the start of the new season.

So far this summer the club have signed only the 18-year-old forward Gabriel Martinelli despite being linked with a host of names. Arsenal have a smaller budget than the majority of their closest Premier League rivals but have still continued to show reported interest in some key targets.

The Crystal Palace winger Wilfried Zaha, Kieran Tierney of Celtic and the young Saint-Étienne defender William Saliba have all attracted attention from the Emirates Stadium hierarchy this summer. And, with only Burnley, Newcastle, Crystal Palace and Norwich spending less on new recruits so far, the lack of investment is one of the issues highlighted by an alliance of Arsenal supporters’ groups in recent days.

However, speaking before Arsenal’s opening International Champions Cup match against Bayern Munich in Los Angeles, Emery claimed there will be more transfer activity in the coming days as he looks to build a squad to take the club back into the Champions League.

“We are working, the club is working with the possibility to sign some new players to help us,” he said. “We are doing a lot of meetings with the club, with [the technical director] Edu, with Raul [Sanllehi, head of football] and also with Josh and Stan Kroenke on Monday in Denver. We have a clear idea to sign players to help us with quality and in the positions we need.

“We are talking with the patience and with calm because we really want to sign players who can help us with a big performance and also because we think in the team we have very good players and young players and we also need to take the best player in some positions.

“Really, I can say to our supporters that we are going to have a very good team with the players that are there now and also with three or four players who can help us in a few days. Other players can come here to help us.

“We are being very, very demanding and are first speaking about the possibility to sign very big, very expensive players and the first player in our list is our first target. And after, if we cannot achieve that, then the second. But we are thinking every time that they are going to improve our squad.”

Shkodran Mustafi with Emery during a training session. Photograph: David Price/Arsenal FC via Getty Images

Arsenal saw an improved offer for the Celtic full-back Tierney rejected over the weekend with the Scottish champions holding firm over a fee. A move for Zaha now looks dead in the water after an initial approach was rebuffed while a deal for Saliba, which had appeared all-but complete, has now been complicated following fresh interest from Tottenham.

The Real Madrid midfielder Dani Ceballos is another name now linked with north London, and although Emery would not be drawn on whether a loan deal for the Spain international was close, he did admit the 22-year-old is a “very good player”.