The Jordanian prince, one of five hopefuls, wants transparent voting booths used at Friday's congress to find a replacement for Sepp Blatter. This call was rejected by Fifa's election commission.
Prince Ali then took the case to the Lausanne-based CAS, which said on Tuesday that it had asked for a written response from Fifa before deciding whether to invoke “provisional measures” and suspend the poll.
“The request for provisional measures will be decided by CAS no later than the morning of Thursday 25th February 2016,” a court statement said.
An unlikely win by the prince would upend months of build-up to the election which many believe is crucial to salvaging the world body's scandal-tainted reputation.
Fifa faces mounting pressure over arrangements for the vote in which Asian and European contenders Sheikh Salman bin Ebrahim Al-Khalifa and Gianni Infantino are the favourites.
Jerome Champagne, a former Fifa official from France, has demanded that the world body cancel accreditations for the Asian Football Confederation and UEFA saying they will be used to lobby for Sheikh Salman and Infantino.
Prince Ali's Paris lawyers — from the firm Szpiner, Toby, Ayela and Semerdjian — said they first sought Fifa's agreement for CAS to decide the voting booth issue, but were rejected.
They then asked CAS to suspend the election.
Pictures of ballots?
The prince has paid for transparent voting booths to be sent to Zurich for the congress.
“Only a transparent booth can prove that each voter is following his heart and conscience and that there are no forced votes, by preventing voters taking photos of their voting paper to prove that they have followed voting instructions,” Renaud Semerdjian, one of the lawyers, told AFP.
Fifa responded by saying that mobile phones and cameras would be banned in the voting booths so that no photos could be taken.
With the election campaign reaching a tense peak, the prince and Champagne have led complaints about the arrangements. The fifth contender is Tokyo Sexwale, a South African tycoon and politician.
Champagne called on Fifa to cancel the accreditation of UEFA and AFC observers and indicated he could also go to CAS.
Champagne accused Sheikh Salman, the AFC president, and Infantino, UEFA general secretary, of seeking to “swamp” Friday's vote with supporters.
Champagne said the observers would give an unfair advantage to Sheikh Salman and Infantino.
The former Fifa deputy secretary general said he had discovered with “stupefaction” that AFC and UEFA observers had been accredited “at the very moment when these two confederations are in their final push in favour of their respective candidates.”
He added that those accredited were mainly members of Sheikh Salman and Infantino's campaign teams.
“It is clear that this reveals the objective to swamp the Congress hall with confederation employees able to access the voting FAs and their delegates,” he said in an official complaint to Fifa's electoral committee.
He called on the committee to cancel “these unfair and undue privileges” and warned of other action if there was no response by Tuesday.
Fifa's 209 member associations are to vote for a new leader as the world body seeks to recover from multiple scandals that has seen 39 football officials and business executives charged with corruption by US authorities.
Two companies also face charges.
Swiss prosecutors are investigating Fifa's management and the attribution of the 2018 and 2022 World Cups to Russia and Qatar.
Blatter and UEFA president Michel Platini were suspended for eight years by Fifa over a two million dollar payment that Blatter approved for the French football legend.