"The Greek FA (EPO) has taken a clear position against a candidacy of Gianni Infantino," EPO President Makis Gagatsis told reporters.
"We saw things happen at the World Cup that are not acceptable to football public opinion. Then... came a programme to sell World Cup rights and we are clearly against it, so we withdrew our support of the FIFA president."
He was speaking after a meeting of the UEFA Executive Committee in the northern Greek city of Thessaloniki, with a "legends'" five-a-side game held in the city centre to promote UEFA's grassroots programme.
UEFA president Aleksander Ceferin was also present at the event but did not talk to media.
Infantino has been under mounting pressure ever since he unveiled a proposal to sell a commercial stake of the World Cup to private investors. The plan prompted fierce opposition, with UEFA, the Asian Football Confederation and North America's CONCACAF among those calling for change at the top of FIFA.
FIFA quickly abandoned the plan and apologised to member associations for mistakes made, but its leadership reaffirmed support for Infantino after a crisis meeting in August in Morocco.
UEFA has been among the staunchest critics of Infantino and have said a change in leadership is now necessary given the loss of trust in Infantino, who is planning to run for re-election in March.
"We have to take care of football," Bierhoff, who was Germany's national team director for 18 years until 2022, said.
"It is already commercial but it is a property for all of football. The world views may be different but in the last weeks and months a lot happened so that we have no trust any more that it will be going in the right direction."
Infantino has weathered the opposition against him since he apologised to FIFA members in August over errors surrounding the abandoned proposal but has since declined to discuss the fallout publicly.
Sources have told Reuters his critics are now having to rethink their strategy.
They have until mid-November to name a rival presidential candidate but so far there is no clear frontrunner.
On Saturday, Danish football chief Jesper Moller, a member of UEFA’s Executive Committee, said he would continue working with European colleagues to find a candidate who could command a majority.