Benitez refused to rule out a move for Perez after his team's last pre-season friendly.
"We know what we need and will try to do this until the end of the transfer window", Benitez is quoted as saying by The Shields Gazette.
Benitez added: "Am I happy with the way we have done things? No".
Speaking to Sky Sports, Benitez said: "I am not happy but at the same time for me it's a challenge". I try to manage and to improve the squad with the players who are available to make sure we are stronger than we are now.
"It's very hard (for me to walk away)".
"I am trying to do my best right now. It is something you cannot control but at the moment I am fully committed to doing the best that I can".
Merson said of Newcastle, "They won't be happy with this, but they haven't really recruited yet".
It is the shadow of history that is causing concern, and there remains an undercurrent of 2008, when the Newcastle owner Mike Ashley failed to back the then-manager Keegan.
Outlining discussions he has held with Wenger, Benitez told reporters: "I said: 'Listen, we have to talk.' And he said: 'Do you have some money?' Obviously, we like good players, but it's too soon to talk about that".
"If we are still in the race it's because we believe there's a possibility and we will continue to fight because the truth is the player is looking forward to joining us".
However, The Chronicle reported that Arsenal want £13.5m for their player, while his agent thinks that £10.8m is a fair price. But the most they've spent on any one player is the £10m for Championship winger Jacob Murphy.
Looking at the bigger picture however, the Gayle injury issue highlights the need for the club to boost their options ahead of the new season.