The Germany international ended his four-year association with Bayern Munich to make the move to Serie A in July, having fallen behind Mario Mandzukic in the striking pecking order at the Bundesliga champions.
But the 28-year-old has revealed that he was approached by Real over a potential move to La Liga before completing his transfer to Italy.
"Ancelotti was interested," he told Kicker. "I was flattered, because my whole family are fans of Real Madrid.
"I thanked him for his interest and told my advisor that I just wanted to go to Florence.
"For me it was clear - I wanted to keep giving everything again properly and not to just play half the games in a top team and obtain many titles. I want to play Sunday, Wednesday, Sunday."
Gomez made just nine Bundesliga starts last term as Bayern lifted the German title, DFB-Pokal and UEFA Champions League.
The former Stuttgart forward has started both of Fiorentina's first two league games of the season, and netted twice in Sunday's 5-2 victory over Genoa.
