Sepp Blatter highlighted the 25,000 tests carried out in football last year
Football's place in the Olympics could be under threat if its chief bodies do not comply with the World Anti-Doping Agency's (Wada) "whereabouts" code.
Wada wants football to join sports like athletics and provide players' location for one hour each day of the year.
World football body, Fifa, and its European counterpart, Uefa, said they wanted to respect players' privacy.
"The sport could be removed from the Olympics," Wada general secretary David Howman told BBC 5 Live.
He added: "There is a clause in the IOC (International Olympic Committee) charter that states this - it falls in the IOC jurisdiction and not ours."
The initial statement from football's governing bodies said: "Fifa and Uefa do not accept that controls be undertaken during the short holiday period of players.
The feedback we have received from the overwhelming majority of other sports, but also from athletes and all those who support doping-free sport, strongly contradicts Fifa's and Uefa's stance
John Fahey Wada president
"Fifa and Uefa want to draw attention to the fact that, both on a political and juridical level, the legality of the lack of respect of the private life of players, a fundamental element of individual liberty, can be questioned.
"Every year, the footballing world organises between 25,000 and 30,000 doping controls and is committed to fighting doping in football with all of its means.
"In a spirit of collaboration in the fight against doping, Fifa and Uefa therefore ask Wada to reconsider its position on the 'whereabouts' rule."
John Fahey, president of Wada, responded: "One of the key principles of efficient doping control is the surprise effect and the possibility to test an athlete without advance notice on a 365-day basis.
"Alleging, as Fifa and Uefa do, that testing should only take place at training grounds and not during holiday periods, ignores the reality of doping in sport.
"Experience has demonstrated that athletes who cheat seize every opportunity to do so and dope when they believe they won't be tested.
"Some substances and methods disappear quickly from the body while keeping their performance-enhancing effects. Anti-doping organisations must therefore be able to test athletes at all times in an intelligent fashion."
It is not a question of not fighting doping but one should not really go for a witch-hunting
Sepp Blatter Fifa president
Fifa's executive committee had already opposed the 'whereabouts' rule last week and that decision was echoed by Uefa's executive committee at a meeting in Copenhagen on Tuesday.
The governing bodies want to exempt footballers from the individual responsibility and claim that the Wada guidelines are not suitable for team sport.
"Fifa and Uefa wish to point out the fundamental differences between an individual athlete, who trains on his own, and a team sport's athlete, who is present at the stadium six days out of seven, and thus easy to locate," read the statement.
"Fifa and Uefa therefore oppose the individual 'whereabouts' rule, and want to see it replaced by collective location rules, within the scope of the team and within the stadium infrastructure."
In a statement, Wada responded: "The new standard provides team sports with the opportunity of submitting the whereabouts of their relevant athletes on a collective basis as part of team activities.
"This specific point was the result of requests from and extensive consultation with team sports, including Fifa, and was specifically made to accommodate team sports."
Fifa president Sepp Blatter, who sits on Wada's board, said football's world governing body had teamed up with other team sports, such as basketball, ice hockey and rugby union, to oppose the rules.
"We are a little bit surprised that through certain declarations [Wada] say there will be no exceptions made," he said.
"It is not a question of not fighting doping but one should not really go for a witch-hunting because witch-hunting has never led to a positive result."
The Professional Footballers' Association (PFA) has already signalled their opposition to the rule.
PFA chief executive Gordon Taylor said: "We feel to invade the privacy of a player's home is a step too far."
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