The cost has been estimated at a minimum of £12million, rising to £20m, but Benitez insisted support from his American benefactors was as unwavering as when they took over in the summer.
"Money always matters but is not the most important thing and that came across when I had a meeting with the owners last week.
"Progressing in tournaments, and the prestige of winning trophies, counts just as much and Tom and George both felt the same way. We spoke about lots of subjects in our 45 minutes together but not money.
"We spoke about the team, our plans for the future, the stadium, everything, and I came away feeling we were thinking along the same lines. There was no sense that I was under pressure. They want to win trophies as well but they were happy. In fact, they were every bit as pleased as when I first discussed our plans with them last July.
"They want to win trophies, just like I do, but they appreciate that when you're trying to change things and improve it can't all come together in an instant. They're not the type to press the panic button. We have a very good relationship and that makes it easier for everyone."