Qaddoura Faris, who heads the Palestinian Prisoner's Club, said one of the four, Mohammad al-Barq has been on a hunger strike for 119 days, the Palestinian news agency WAFA reported.
Barq and another prisoner, Hassan Safadi, are both reported in critical condition. Safadi has been on a hunger strike for nearly three months.
Barq was taken to a civilian hospital in central Israel on Monday after he collapsed at a Ramallah prison clinic, the Palestinian Ma'an News Agency reported.
A prison spokesman told Ma'an Sunday that Israel has agreed to Barq's request to be deported to Egypt.
No date has been set for the transfer to take place.
He has been imprisoned without charge or trial since July of 2010.