Brentford chairman Eddie Rogers told the Richmond and Twickenham Times the club was "seriously considering" the alternative proposal.
"If the Gillette site could be made to work financially we would be delighted to explore that," he said.
The Gillette side is 11 acres, as opposed to seven at Lionel Road and would therefore be more expensive.
Rogers added: "Lionel Road remains our main target, though the progress on this project is slow."
Whichever scheme Brentford choose, they are set to remain at their present Griffin Park ground for five years.