Emergency services rushed to the home of the former midfielder on Thursday but were unable to save his life.
Zaqout had recently been working as a coach and as host of a Palestine sports programme in Gaza.
Khaled Zaher, a Gaza sports journalist told Reuters: "Palestine has lost one of its best players, he may have been the best midfielder we ever had."
The 49-year-old was a part of the Palestinian team that played a friendly against a team of French stars that included UEFA's president Michel Platini in 1994. Four years later, the Palestine football team was accepted into Fifa.
Last month Mona Dabdoob, from the Palestinian Players’ Federation, presented FIFA chiefs with a dossier of restrictions and attacks from Israel on Palestinian football as they met in Brazil.
Fifa ruled out sanctions against Israel but said it would monitor the country's alleged violations of Palestinian football, including preventing players from travelling to and from matches.
In January two young Palestinian footballers from Abu Dis FC, Jawhar Nasser Jawhar, 19, and Adam Abd al-Raouf Halabiya, 17, were reportedly shot by Israeli snipers, beaten up and had dogs set on them as they walked home after training.
"There was no alarm, no identification or warning," Jawhhar told Vice.
In an interview with the website Adam said that he was shot first in the leg. As Jawhar tried to drag him to safety, he was shot repeatedly in the hand and leg — 11 times total. Adam was shot once in the knee and two times in the other leg. The teenagers told the website that as they lay screaming, Israeli forces set a dog on them.
"They hit my head with a gun and they broke the leg with a gunshot in. They forced my leg backwards until it snapped. They were joking and laughing." Adam said.
Israeli police maintain that the teenagers were moments away from attacking the nearby police base.
Medical reports indicated that Jawhar was shot with 11 bullets, seven in his left foot, three in his right, and one in his left hand. Halabiya was shot once in each foot. The two were taken to Ramallah governmental hospital before being transferred to King Hussein Medical Center in Amman.
After transfer to Amman the teenagers were informed that they would never play football again.
On March 10 Saji Darwish, Birzeit student and player for Beitin FC, was shot dead by soldiers near the West Bank settlement of Givat Assaf, close to Ramallah. It was alleged that he was throwing stones at vehicles belonging to Israeli settlers in the area.
Meanwhile as of late Saturday, Gaza health ministry officials reported that the death toll has now risen 1,712 Palestinians. Among those killed 398 were children, 207 women and 74 elderly.
There has been 63 Israeli soldiers killed as well as three Israeli civilians killed.
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