Mikel Arteta has already spent heavily in the transfer market this summer and the Arsenal boss has hinted there could be more arrivals.
Arsenal have spent nearly £200million already this summer with the arrivals of Declan Rice, Jurrien Timber and Kai Havertz.
But after finishing second behind the champions Manchester City, Arteta is desperate to close the gap on his former club.
"Let's see," he said pitchside at George Mason University in the United States.
"It's a lot of time still in the market and a lot of expectations are in some of our players as well, so we will have to see and how things develop in the next couple of weeks.
"We will be alert, there's still time do things, there's still time as well for exits obviously. I'm sure things will move."
Arsenal have crossed the Atlantic at an exciting time for football in North America, where Lionel Messi's mammoth move to Inter Miami should take the sport to new heights.
"I think the attention it's going to do, the level, the attraction, I think it's incredible for the league to bring a player with such a status here," Arteta said.
"It tells you the ambition of the league, where they want to take it and the direction this has taken I think is extremely positive for the league."
On facing Rooney's All-Star team at Audi Field on Wednesday, the Arsenal boss added: "Great, a lot of expectations. It'll be a special atmosphere and something we haven't done before so looking forward to it."
Speaking about Rice, who was also a target for Man City, Arteta said: "I see him like a lighthouse – that he is willing to put light in others and improve others and make the team better and that is a huge quality.
"For me, to be a midfielder you have to have that and he's got it 100 per cent.
"The way he talks and presents himself, the ambition he has and the passion towards the game. That is exactly what we needed.
"It's his leadership, his aura, the experience he already has in the league he is going to bring and the team to a different dimension I think."
