After Real recorded a 5-0 win against Viktoria Plzen in the UEFA Champions League group stage on Wednesday, the pair said they have been happy with Solari's work since he replaced Julen Lopetegui at the end of October.
"Julen is a great coach, but we are with Solari now and playing with more confidence," Benzema said, per ESPN FC's Dermot Corrigan. "For me, he should stay until the end [of the season]."
On Movistar Plus, Casemiro added (h/t Corrigan): "We are facing up with Solari as coach of Madrid. People can talk about whether someone else is coming or not, but we are showing him respect as Madrid's first-team coach. If things are going well, why not give him a chance?"
Right-back Alvaro Odriozola was also asked about the possibility of Solari's permanent appointment:
Solari has rode his luck at times as Los Blancos boss. In their 2-0 win over Real Valladolid on Saturday, things could have been different, as the visitors hit the crossbar twice when the scores were level, while Vinicius Junior's opener went in via an enormous deflection from Kiko.
Plzen hit the bar early themselves on Wednesday, and Sergio Ramos was perhaps fortunate to escape punishment for catching Milan Havel in the face with an elbow.
The Spain international apologised for the challenge after the match:
Los Blancos maintained control of the game after getting themselves in front, though.
Benzema scored twice either side of Casemiro's header before Gareth Bale and Toni Kroos got on the scoresheet to complete the rout.
The comfortable win continued Solari's strong start in terms of results and goals scored:
Per Corrigan, the coach was asked whether Real Madrid's crisis was over, to which Solari quipped: "You must not know Real Madrid. We live in permanent crisis all the time, even when we are winning the Champions League."
Real's outlook does seem much better after three successive victories and clean sheets, but those results came against lower-level competition in Plzen, Valladolid and Spanish third-tier side Melilla in the Copa del Rey.
Los Blancos will face a sterner test in their next match, as they travel to Celta Vigo, whose record of 20 goals in 11 La Liga matches this season is bettered only by those of Sevilla and Barcelona.
If they come through it with the players remaining positive, Solari may well be given the rest of the season to prove himself at the Santiago Bernabeu.