Authorities said that Seif al-Din Mohamed Mostafa, 58, is fighting his extradition by also applying for asylum to stay on the island.
His asylum request is being reviewed by the immigration department while extradition proceedings go ahead.
"The suspect has asked for asylum and this procedure will run in parallel with the court hearing on extradition," an official source told AFP, speaking on condition of anonymity.
Cyprus has approved a request from Cairo to extradite Mostafa, and a hearing is scheduled to take place on April 22.
Mostafa reportedly argues that he faces the death penalty if sent back to Egypt.
Nicosia expects Cairo to state in writing that he will not face the death penalty at a trial in Egypt, local daily Phileleftheros said on Tuesday.
Mostafa, currently in police custody, is accused of using a fake suicide belt to seize the Alexandria to Cairo flight on March 29 and force it to land at Larnaca airport.
Cyprus is expected to try to fast-track the extradition process, which could take several weeks.
Mostafa is expected to remain in custody until the extradition papers are ready.
The Egyptian state prosecutor's office had asked for him to be handed over under a 1996 bilateral extradition treaty.
Described by authorities in Cyprus as "psychologically unstable", Mostafa has said he acted out of desperation to see his Cypriot ex-wife and children.
Cypriot prosecutors said he faced possible charges of hijacking, kidnapping, reckless and threatening behaviour and breaches of anti-terror legislation.
Police said Mostafa gave a voluntary statement admitting to the hijacking.
His ex-wife has been quoted by Cypriot media as describing their five years of marriage as a "black period" in her life.
The hijacking ended peacefully with Mostafa's arrest.
Most of the 55 passengers were quickly released after the plane landed, but some escaped only minutes before the six-hour standoff ended.
