Mido is currently on loan at Zamalek from Middlesbrough, but is keen on making a return to England in the winter.
Zamalek said last week that the 26-year-old striker will fly to England in order to negotiate a January move with a Premiership club, which eventually seems to be the Hammers.
"It would be one of the most amazing deals of all time. He doesn't want to be known as a 'has been' of English football, so he willing to come here to play for a nominal fee, just £1,000-a-week," Sullivan told ESPNsoccernet on Monday.
"He is a rich boy, even though he is still only 26, and he told us he doesn't need the money, but he wants to prove something in English football.
"He is a Middlesbrough player who is on loan back in his home country Egypt, but he is desperate to show people here what he can do. We are hoping to clinch this deal today."
Mido accepted a significant pay-cut to his Boro salary before moving to old club Zamalek in the summer, but his six-month stint in Egypt has been anything but successful.
The former Tottenham hitman has only scored one goal for Zamalek and has been often criticized of being out of fitness.