The case of Bahraini footballer Hakeem al-Araibi "has become an absolute emergency", according to campaigners.
The 25-year-old holds refugee status in Australia after fleeing his homeland in 2014, but is being held in Thailand.
Former Australia captain Craig Foster, who is leading the effort to secure Al-Araibi's release, met with Fifa officials on Monday.
But he warned that Bahrain pressing ahead with plans to extradite Al-Araibi had "escalated the issue".
The Arab kingdom says that extradition proceedings are now "in process".
In a statement, interior minister Sheikh Rashid bin Abdullah al-Khalifa also insisted "external interference in the internal affairs of Bahrain is unacceptable".
Fifa general-secretary Fatma Samoura has "strongly urged" the authorities in Thailand and Bahrain to "do the right thing" and ensure Al-Araibi can go back safely to Australia "as a matter of urgency".
The Asian Football Confederation's (AFC) senior vice-president Praful Patel has also written to Thailand's prime minister, Prayut Chan-o-cha, to ask for Al-Araibi to be returned safely to Australia at "the earliest possible opportunity".
But the AFC had previously been criticised for refusing to take a position on the matter, saying the case is not the responsibility of its President - Sheikh Salman - a Fifa vice-president and a member of the Bahrain royal family - because of a potential conflict of interest.
Salman was the target of criticism by Al-Araibi in 2016, but according to Fifa statutes, "human rights commitments are binding on all Fifa officials when exercising their powers and competences." Salman is now facing calls to resign.
Al-Araibi fled to Australia in 2014, where he was granted political asylum in 2017, and plays for Pascoe Vale in Melbourne.
In 2014, he was sentenced in his absence in Bahrain to 10 years in prison for vandalising a police station. He denies the charges, with campaigners from the Bahrain Institute for Rights and Democracy (BIRD) saying he is at grave risk of torture if he is deported.
He was on honeymoon in Thailand when authorities detained him at a Bangkok airport on 27 November last year.
Amid mounting pressure from across the world, Al-Araibi's plight has become a test case for sporting bodies' recent strengthened commitment to human rights.
In 2017, Fifa adopted a landmark human-rights policy and, along with the International Olympic Committee (IOC), has expressed support for Al-Araibi.
Foster - and world players' union FIFPro - have suggested Fifa should threaten sporting sanctions against Bahrain and Thailand.
Having met Fifa general-secretary Samoura, Foster said: "We agreed that this has now become an emergency situation requiring an escalation across the board from all stakeholders.
"We also agree that Fatma and Fifa are going to escalate the issue to the highest level of both countries.
"The human rights policy of Fifa is an incredibly important tool in this situation and we're delighted that Fifa has demonstrated again their commitment to ensuring that every stakeholder in football will apply the absolute maximum leverage.
"[Over] the next five days we want to see absolute progress and that means Hakeem Al-Araibi being released.
"We feel the urgency and emergency of the matter is so grave right now that all of sport has come out in favour of Hakeem."
Former England player Gary Lineker has tweeted in support of the #SaveHakeem campaign, and a petition calling for al-Araibi's release has so far received 50,000 signatures.