Despite having scored 202 goals for Madrid, Benzema was among the players criticized by fans and local media during the team's hard stretch under Lopetegui, the former Spain coach.
While Real have yet to make a marked improvement in overall performances under former midfielder Solari, they have enjoyed far better fortunes than in the final weeks under Julen Lopetegui, who was sacked two weeks ago after the humiliating 5-1 defeat to Barcelona.
Fresh from a midweek Champions League brace against Viktoria Plzen - his 200th and 201st goals for the club - Benzema had a real spring in his step against Celta.
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The 42-year-old has since led Real to 4 wins in 4 games, the best start of any manager in the club's history.
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Speculations that first choice managers including Antonio Conte and Mauricio Pochetino have turned Perez down seem to put the caretaker manager in the prime position to get the job, but Solari's relative inexperience at this level puts him at a slight disadvantage.
"He has done excellently", Madrid club director Emilio Butragueno said on Sunday night.
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"It was a very complicated game and we also had setbacks with injuries, (but) we had personality and character". If not, the progress the team has made under him will be seriously questioned and the pressure will again be on the club to bring in an experienced coach. He also made the team play, he created space, he defended.
"The important thing is to do what is necessary for the good of the team, everything else doesn't matter", Solari said.
Both players will thus be unable to play for their countries in the forthcoming global break and they will miss their side's last two Champions League group matches, as well as at least three Liga Santander matches.
Alvaro Odriozola, who has been one of the stars of the Argentine's run to date in charge, said following the weekend win over Celta: "He is a great coach and of course we want him to stay in charge".
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