"I only found out about the offer after the club had turned it down," the 25-year-old Germany international told Sport Bild weekly in an interview.
"But it wouldn't have mattered anyway. I am already at a top club and I am playing where I always wanted to."
Chelsea instead ending up paying 50 million pounds (59 million euros, 80 million dollars) for Liverpool striker Fernando Torres just before a transfer deadline, smashing the British record.
Gomez joined the defending Bundesliga champions in 2009 from Stuttgart in a 30-million-euro move. After a lacklustre start, he is the Bundesliga's top striker this season, with 16 goals to his name.
Torres, by contrast, found the back of the net nine times before his move to Stamford Bridge.