Clarkson told the Sun, for whom he writes a regular column, that an unnamed BBC executive had "asked if I'd come back to Top Gear" last week.
But Clarkson said he refused: "It would have been impossible to make the show I'd want to make," he said.
The BBC has named Chris Evans as the new host. "We haven't offered another Top Gear contract," a spokesman said.
"The BBC had placed on record its thanks to Jeremy for his broadcasting on the programme and wish him well for the future."
Clarkson, who was sacked for punching a Top Gear producer in March, told the Sun that returning to the Top Gear role "was never an option".
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