Barnet could leave Underhill after talks with the council over adding extra seating reached deadlock. The Conference champions need to add 1,000 more seats to comply with Football League regulations.
Chairman Tony Kleanthous failed to get backing from Barnet Council to have the work done and said: "We feel there is no point pursuing the current dialogue.
"To safeguard the future of Barnet FC we have no option but to explore other avenues, including ground-sharing."