The Toronto and Region Conservation Area board voted Friday to defer any action on the mayor's request until further study has been done.
The public land — the site of a recent confrontation between the mayor and a Toronto Star reporter — is studded with mature trees.
Ford wants to purchase it so he can put up a security fence behind his home.
His plans became more widely known this week after his run-in with reporter Daniel Dale, who Ford said was spying on his property.
The Star said Dale was on public property researching a story about Ford's bid to buy the land — not spying on or harassing the mayor.
Police have launched an investigation into the incident and Ford has said he will not speak to any media if Dale is present.
Coun. Glenn De Baeremaeker was the lone board member to vote against Ford's request on Friday, saying if one resident is allowed to buy a piece of the park, others will want do the same.
The city will now issue a report to be looked over in June.
If the sale is approved, members of the public will be given a chance to speak on the matter before a final vote by the board.
De Baeremaeker said he doesn't see why the mayor needs to buy more property.
"I don’t think that buying more parkland from the public is going to make the mayor’s family safer. I think perhaps building a better fence will make the mayor's family safer," De Baeremaeker said.
However, he said such public land has been sold before in special circumstances.
(AM640, CFRB, The Canadian Press)