Navarro spoke to Spanish media after Sevilla presented Jon Guridi, Juan Iglesias and Arouna Sangante at the Ramón Sánchez-Pizjuán, with goalkeeper Odysseas Vlachodimos also joining on a season-long loan extension from Newcastle.
Asked directly about the club's financial position, Navarro was blunt about the size of the challenge still facing Sevilla this summer.
"We don't have registration capacity for any player as things stand, unless we transfer a player or free up wage room. From there we'll be able to register both the four players who are already with us and those who are still to come," he said.
That admission underlines the pressure on Sevilla to offload squad members, with Nianzou and Akor Adams closest to the exit door.
"We're in open negotiations with two clubs. Right now, until it's made official, obviously anything could happen in either direction. In football, until everything is signed and announced, you can't take anything for granted because it can be subject to change," Navarro explained.
Rafa Mir is another player Sevilla are working to move on.
"We're working, as we are with some of his team-mates, to find the best exit for both Sevilla and Rafa," he said.
The wage-limit squeeze also extends to defender Marcao.
"The club's objective isn't to free up wage room, it's to achieve sporting objectives. Obviously we have to comply with the economic control regulations set by La Liga. Marcao is part of the squad and with the market still open he could stay or he could leave," Navarro said.
Joan Jordán is among the players told he no longer forms part of Luis García Plaza's plans.
"We don't know what action his representation agency wants to take. With Joan, as with other team-mates, we had a personal meeting when they returned from holidays and we explained the situation openly. They're currently not part of the sporting plan for next season and we're looking for an exit for them. In the end, they're assets of the club, we can't forget that, and Sevilla has to defend its rights and its players. They have to be supported and given the facilities to keep training," he said.
Sevilla have also trimmed their forward line, going from four strikers at the end of last season to just two, Akor Adams and Isaac Romero, currently on the books.
"Communication with the coach is basically daily, several times a day. We finished the season with four forwards and today we have two in the squad, Akor and Isaac. From there, players will come and go and the important thing is that on 1 September we have the most competitive squad possible to face the season," Navarro said.
Despite the registration freeze, Navarro insisted Sevilla's transfer business so far has been positive, with the priority now shifting firmly toward departures before any further incomings can be confirmed.
Navarro's remarks, relayed by Spanish outlet Sevilla Actualidad following Wednesday's press conference, also touched on goalkeeper Patrik Mercado, whose proposed €6m move remains unresolved after a knee injury complicated his medical.
"An agreement was reached for a possible signing. Certain conditions have to be met and until they are, it can't be determined whether he'll be a Sevilla player," Navarro said, adding that no fixed deadline had ever been set for the medical to take place.