Speaking at UEFA's annual Congress in Belgrade, Infantino said that the reported peace deal is the perfect opportunity for Russia to return to the international football community as soon as possible.
"Because of politics, the Serbia team was denied access to the European Championship. They certainly had a team to win, but they were denied access.
"We have always to try to use football to bring people together, to bring countries together, especially in our world which is divided.
"As talks are going on for peace in Ukraine, I hope we can soon move to the next stage and bring back Russia in the football landscape, because this would mean everything is solved.
"That is what we have to cheer for, that is what we have to pray for, because that is what football is about."
UEFA president Aleksander Ceferin also spoke about the need for unity in European football despite the devastation on both sides of the conflict.
“We are told that we have never been so divided,” he said in his address to the Congress.
“Every day we hear what feels like a non-stop refrain – us versus them.
“When we hear this day in and day out, it’s easy to believe, but let me tell you my friends, this division is but an illusion and a terribly common tactic, a deliberate and obvious ploy by those who seek to divide us, to divide and conquer.
“European football must continue to stand as a model for unity in this increasingly divided world.”