It's after Los Blancos beat Victoria Plzen 5-0 in the Champions League last night with the Benzema grid brace and the addition of assistance in the Czech Republic.
Real have won all three games under the solar – which is still the temporary boss since being a temporary manager following the hacking of Jules Lopetegui.
In Los Blancos he wanted to appoint the former boss of the Cecile, Antonio Conte, instead of the Spaniard, but he flinched from the Italian after Serge Sergey Ramos publicly expressed his reservations.
Arsene Wenger, Maurizio Puccini and Tino Mourinho have all been linked ever since, but it seems more and more that Solari – who was Real Madrid Castilla boss for two years – will be given a full-time job at least until summer.
The former real midfielder has steeredied the ship since coming in with the side scoring 11 goals and conceding none of his tenure so far.
And Nazmeh offered his support at 42 if he was given the job until the end of the season and insisted that he had to "stay" because he would be useless for a month.
"Sure, why not, we're all right with him," Benzema said after winning the Plzen, as Marca had quoted him.
"I do not see a coach coming in a month or two, so for me Solari should stay until the end of the season at least.
"He's a great coach, now we have more confidence and we're going to compete.
"I am happy with the victory and the goals.
"And with good game management because it was difficult, but confidently we did good things."
And Real Madrid right back Alvaro Odriozola is also keen on Solary to be kept on.
"Solar is an excellent coach who was also a very good player," he declared.
"We focused on working with any coach but we fought to death for Solari.
"It was a great night, we needed a match like that to restore confidence, we're leaving here with a very good feeling."
Discussing his future at a press conference to present the clash with Plzen, the manager looks like he still has not settled his future yet.
Solar said: "I am committed to my job, whether it will be two days, or a week, exactly the same."
Real face Celta Vigo in La Liga in their next game on Sunday (7.45) with Real required to announce a regular appointment only days later.
This is with football federation football rules that states that clubs "are obliged to find a new coach who is authorized to category within a maximum time frame of two weeks" after the administrative vacancy is available.