The Palestinian president's condition has seen a "clear improvement" after he was taken to hospital with a fever, a politician has said.
Mahmoud Abbas was taken to hospital on Sunday with a fever, just days after undergoing ear surgery.
The 83-year-old leader has endured a series of recent health scares which have revived anxiety over a potentially chaotic, and even bloody, succession battle that could further weaken the Palestinian cause.
Ahmad Tibi, an Arab politician in Israel's parliament with close ties to Mr Abbas, told Israeli Army Radio that he could be discharged as early as Tuesday.
He did not elaborate on Mr Abbas's condition nor say why he thought he was expected to be released.
Palestinian officials had said on Sunday that Mr Abbas has pneumonia and was on a respirator, receiving antibiotics intravenously.
They said he was conscious and lucid.
Mr Abbas, who is a heavy smoker and overweight, has a long history of health issues, ranging from heart trouble to a bout with prostate cancer a decade ago.
The condition of Palestinian President Mahmoud Abbas, who was hospitalised for a third time in a week, is reassuring and his tests are normal, the director of the hospital treating him says pic.twitter.com/uZ554DCYFV— TRT World Now (@TRTWorldNow) May 20, 2018
Two years ago, he underwent an emergency heart procedure after suffering exhaustion and chest pains.
More recently, a cardiologist moved into the presidential compound in Ramallah to monitor the longtime leader after a mysterious hospital visit in the United States, following Mr Abbas's address to the United Nations Security Council in which he appeared weak.
Mr Abbas, who insists he is fine, has refused to designate a successor.
But after more than a decade of avoiding discussion of the post-Abbas era, Palestinian officials acknowledge that they are concerned, and potential successors are quietly jockeying for position.
Mr Abbas took over as a caretaker leader following the death of Palestinian leader Yasser Arafat in 2004, and was elected for what was supposed to be a five-year term the following year.
He has remained in firm control since then, governing parts of the West Bank, while a political split with rival Hamas - the Palestinian militant group that in 2007 seized the Gaza Strip - has prevented new elections.