The 42-year-old was handed the Real reins on a caretaker basis after the departure of Julen Lopetegui and seems to have made an immediate impact, with back-to-back wins for Los Blancos under his guidance.
There will be another test of his credentials on Wednesday night as the capital club travel to play Czech outfit Viktoria Plzen in the Champions League.
It has been suggested the Argentine has his eye on a permanent coach's role with Real but Solari has made it clear he is just focused on keeping the winning run going.
"I am committed to my role, whether that be for two more days, or a week, just the same," he said at Tuesday's pre-match press conference.
"In football the solutions and problems are never just one thing, whether it is going well or not. We have played two difficult games, which we had to play well to win.
"You do not win games if you do not do things well. We have to do the same tomorrow (Wednesday) in a different competition."