The visit to the Estadio Municipal de Balaídos represents the sternest test of Solari's brief reign so far, with the Argentine former midfielder having won all three games since taking over from the sacked Julen Lopetegui.
Real, sixth in the table and seven points behind leaders Barca, have struggled at the Galician side's intimidating stadium in the past, though, and could only muster a 2-2 draw at the venue last season.
Local media reports suggest a victory would complete an impressive audition for the role with a promotion, but Solari insists he is focussed on three points rather than his future.
"I'm just thinking about the next game despite everything," he told a news conference. "I can only look to the next link in the chain, and the most important game is always the next one. We are focussing all our efforts on this weekend's match.
"I know it's a cliché, but football is about the here and now, and it's not a bad philosophy to go by. We'll see after that."
Elsewhere on Sunday, table-toppers Barcelona host Real Betis as they look to maintain the pace in their title defence, but it remains to be seen whether the Catalans will have Lionel Messi back from injury for the match.
The forward fractured his arm last month and while he was not missed in their Clasico victory over Real, his absence was noted as the defending champions eked out a last-gasp win at lowly Rayo Vallecano last week.
Messi was included in the party that travelled to Milan for their midweek Champions League draw with Inter, but was omitted from the match-day squad as they secured a place in the last 16 of the competition.
"He is training, but it's not the same as playing in a top-level game with collisions and intensity, so we don't want to take any risks with him," coach Ernesto Valverde said.
"The objective is always the same and that's to get the three points," Valverde added. "We always want to retain possession and have control of the game. It's good because the side are showing their worth."
It is also shaping up to be an interesting weekend for the chasing pack, with only one point separating the sides from second to fifth place, starting on Saturday evening when fourth-placed Atletico host struggling Athletic Bilbao.
Fifth-placed Alaves then host bottom-of-the-table Huesca in Sunday's early kickoff, before third takes on second when Sevilla host Espanyol later on.
(Reporting by Joseph Cassinelli; Editing by John O'Brien)
