Fifa has ordered Russia to complete their upcoming matches without their flag, anthem and as the Football Union of Russia in neutral territory, following the invasion of Ukraine.
Several nations have announced that they will refuse to play Russia, including England, as well as Poland, the Czech Republic and Sweden.
World Cup play-offs would see Russia face Poland then either the Czech Republic or Sweden if they win - and are due to be played in March.
Russian President Vladimir Putin launched a military invasion of neighbouring Ukraine on Thursday.
Fifa said talks will take place with other sporting organisations over whether Russia should be expelled from competitions.
"Fifa would like to reiterate its condemnation of the use of force by Russia in its invasion of Ukraine," world football's governing body said in a statement on Sunday.
"Violence is never a solution and Fifa expresses its deepest solidarity to all people affected by what is happening in Ukraine.
"Fifa will continue its ongoing dialogue with the International Olympic Committee, Uefa and other sport organisations to determine any additional measures or sanctions, including a potential exclusion from competitions, that shall be applied in the near future should the situation not be improving rapidly.
"Fifa's thoughts remain with everybody affected by this shocking and worrying situation."
Earlier on Sunday, the Football Association announced England will not play any international matches against Russia at any level following the invasion of Ukraine.
The FA said they "wholeheartedly condemn the atrocities being committed by the Russian leadership".
English football's governing body said the boycott of matches will be "for the foreseeable future".
Analysis
Dan Roan, BBC sports editor
I doubt Poland, Sweden and the Czech Republic will be satisfied with this and I wonder what they think of Uefa backing it. Are there now questions for Uefa's president Ceferin?
Fifa say Russia must play home matches on neutral territory - but who on earth would agree to host them?
This will disappoint those calling for Russia to be excluded but Fifa will say this sounds like a final warning: "Fifa will continue its ongoing dialogue…to determine any additional measures or sanctions, including a potential exclusion from competitions."
Sport continues to react
The International Judo Federation has suspended Russian president Vladimir Putin as its honorary president.
Boxing's world governing bodies the IBF, WBA, WBC and WBO say they will not sanction any title fights in Russia.
Ukrainian tennis player Elina Svitolina will donate prize money to aid efforts.
The world number 15 says
the money will be used to "support the army and humanitarian needs and help them to defend you, our country".
At the Fencing World Cup in Cairo, Ukraine's men's foil team refused to fence against Russia on Sunday.
"This is our protest against the war. We cannot fence against them while our families are in danger, and everybody is in danger," said the team.
Meanwhile, Premier League football club Chelsea said the situation in Ukraine was "horrific and devastating".
The statement came after Chelsea owner Roman Abramovich, the Russia billionaire who is believed to be close to Putin, was criticised for not mentioning the war when he announced he was handing over "stewardship and care" of the club.
Putin is a blackbelt in judo and was awarded the eighth dan, one of the sport's highest honours, by the International Judo Federation (IJF) in 2012. He has also co-authored a book titled Judo: History, Theory, Practice.
"In light of the ongoing war conflict in Ukraine, the International Judo Federation announces the suspension of Mr Vladimir Putin's status as Honorary President and Ambassador of the International Judo Federation," the IJF said.
Announcing their move, the IBF, WBA, WBC and WBO said: "Just as this war has put a stop to boxing in Ukraine, our organisations will not sanction fights in Russia until further assessment of the situation."
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