"Hilal want to sign Zaki in the close season," Nader Shawki told FilGoal.com.
"But my client will not decide whether to accept Hilal's offer until after the Confederations Cup."
The Bulldozer has just finished a season-long loan with English Premier League club Wigan Athletic, where he suffered mixed fortunes.
He impressed in the early stages of the season, notching ten goals for the Latics to top the league scorers' chart for a while.
However, some off-field problems strained his relationship with Wigan coach Steve Bruce, who eventually opted not to sign him on a permanent basis.
"Zaki's priority is to remain in Europe, preferably England," Shawki added.
"There are some European clubs who verbally expressed an interested in signing him but nothing has been official.
"Zaki could join an Arabian Gulf side if he failed to remain in Europe, but it is too early to say that because we still have until the end of the transfer window to make a final decision."
The 26-year-old is currently preparing to take part in the FIFA Confederations Cup with Egypt, who will play in Group B along with Italy, Brazil and the United States.
Several Egyptian players were criticized for joining Gulf sides during the past two years.
The likes of Walid Soliman, who played on loan at Saudi Arabia's Ahli last season, and Ahli Dubai's Hosni Abd-Rabou were blamed by pundits for 'going after money' rather than remaining in the more competitive Egyptian league.