The 56-year-old's side progressed to the last eight on Sunday with a comfortable 3-0 win over Slovakia, thanks to goals from Jerome Boateng, Mario Gomez and Julian Draxler.
Victory sets up a clash with the winner of Monday's match in Paris - the last two teams to knock Germany out of a European Championship.
But, while acknowledging the strengths of both sides, Low has no worries about facing either opponent.
"No, I'm sleeping well," he said after the round-of-16 victory. "Both sides are among the favourites.
"Italy are very strong in defence and good in attack, they had six or seven on the bench in the third game.
"The Spanish have the best attacking game we've seen in recent years, they're different sides but they're among the top favourites."
A lot of focus has been placed on the German boss's team selections, with each member of his line-up impressing against Slovakia.
Though Mario Gotze was dropped and Thomas Muller's Euros goal drought continued, Low suggested he was happy with his forward options ahead of the quarter-final.
"It's not about a false or true nine in our side," he added. "When there is one striker, if nobody follows him, then neither will have any success. It was better against Northern Ireland than against Poland.
"Mario Gomez, Thomas Muller and others were always very deep, were in the opposition area. Then players will always get more opportunities.
"I was happy with Gomez, he's shown some self-confidence in training."