Council leader Alan Williams believes a move to Cricklewood could still solve Barnet Football Club's ground problems.
A multi-million pound groundshare with Hendon FC remains the number one option, he told supporters on Frid.
'We are absolutely committed to this objective ,, league football played by Barnet in this borough,' Mr Williams told around 25 Keep Barnet Alive (KBA) members at a town hall meeting.
'After an extensive survey, the only site that is in the ownership of the council and has the appropriate size and transport, other than Underhill, is Claremont Road Cricklewood. We have worked extensively to try and broker a deal. I think there is still an awful lot of potential.'
But he admitted these proposals were on the backburner after negotiations between the clubs broke down. Financial differences could not be solved, sources have said.
KBA chairman Michael Edwards believes it is up to the council leader to bring Mr Kleanthous and Hendon chairman Ivor Arbiter back to the negotiating table for the £12.7million Cricklewood scheme.
'All he has got to do is get Tony and Ivor to sign up to the deal and I will take him down the pub,' said Mr Edwards.
Mr Kleanthous has until August 1 to raise Underhill Stadium's capacity to 5,500 to meet league requirements. If he achieves this, the league is prepared to be lenient ,, as long as plans for a new stadium are in the pipeline.
Mr Williams agreed Underhill in its current form could not conform to league requirements in the long-term.
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