The Italian announced on Friday that he was willing to agree a takeover with supporters and forgo any profit.
The supporters' group said on Tuesday that they believed Cellino would sell them the club for £30m.
"We've been informed by the lawyers of Cellino he no longer wishes to sell to Leeds fans," LFU said in a statement.
"Our insistence on him confirming his verbal offer of exclusivity in a legally binding agreement has forced transparency on his motives. It is much better that we identify this insincerity now before we spend our shareholders' money.
"This exercise has proved our capacity to adapt to any acquisition scenario very quickly. We now know we have the capacity to do both a minority and majority deal, and it has shown that Leeds fans have a desire for fan ownership.
"We hope that Massimo will treat the club and fans with respect and honour."
Cellino, who is appealing against a second Football League ban, said at the start of the week he would no longer attend matches at Elland Road.
The Whites are 17th in the second tier after winning their first home match since 4 March against Cardiff on Tuesday.
Leeds United chairman Massimo Cellino has told Leeds Fans United he no longer wishes to sell them his majority stake in the club.