Solari's time as the European champions' stop-gap following Julen Lopetegui's sacking will expire over the international break, and club president Florentino Perez needs to decide whether to take the Argentine on permanently.
Real have bounced back under Solari, with Wednesday's 5-0 drubbing of Viktoria Plzen a clear sign of life in the struggling giants.
A win at bouncing Balaidos could well be enough to convince Perez the job should be Solari's, at least until the end of the season, when a more established alternatives could be available.
“We're doing fine with him,” striker Karim Benzema said on Wednesday. “I don't see a coach coming for one or two months, for me Solari has to stay until the end of the season. He's a great coach. Now we have more confidence and we are going to fight.”
Few could begrudge Solari the opportunity to prove himself after stepping up from Madrid's B team to take charge.
Madrid have scored 11 and conceded none since Solari's arrival, against admittedly modest opposition — Melilla from the Spanish third tier, Real Valladolid at home and Plzen.
Luck has also played its part, as Vinicius Junior's deflected shot prevented what looked set to be a stalemate against Valladolid with seven minutes to play. A draw there and Solari's tenure might never have got off the
However it was Solari's decision to bring on the 18-year-old Vinicius, whose youthful exuberance produced an ambitious strike at the end of a weaving run.
Celta will offer a sterner test this weekend. They are the third highest scorers in the division and in Iago Aspas boast the sort of smart finisher Madrid might have signed in the summer.
Aspas' eight goals this term puts him one up on Lionel Messi, who could return on Sunday when league leaders Barcelona host Real Betis after three weeks out with a broken arm.
Messi was included in Barca's travelling squad to face Inter Milan on Wednesday but watched from the ands as his side reached the Champions League knockout stages with a 1-1 draw at the San Siro.
“We wanted him to travel with the team, to train to see how he was,” coach Ernesto Valverde said. Valverde has been afforded the luxury of easing Messi back by his team's strong run without him.
Reaching the last 16 in Europe came after five wins on the bounce, four of them without Messi, including one against Inter at home and the 5-1 hammering of Real Madrid.
A tricky period of fixtures continues against Betis and ends at Atletico Madrid after the international break.
Luis Suarez's with six goals in his last five games have been integral but Jordi Alba has arguably been Barca's player of the season so far.
His form has forced Spain coach Luis Enrique to concede defeat in his mysterious stand-off with the full-back, calling Alba up for the first time on Thursday.
Diego Costa and Koke missed out on the squad with injury as Atletico Madrid head into their clash with Athletic Bilbao on Saturday with a dizzying list of absentees.
Thomas Lemar, Diego Godin and Stefan Savic were also missing for Tuesday's impressive 2-0 win over Borussia Dortmund, in which Jose Gimenez pulled up with a muscle problem.
Fourth-placed Atleti are four points behind leaders Barca and looking to build on the momentum gained in midweek and leapfrog Sevilla and Espanyol, who play each other in Andalusia on Sunday.
By AFP's Thomas Allnut