The Cairo giants are seeking to sign the skillful schemer on a part-exchange deal that will see a couple of players move in the opposite direction.
It's also understood that Ahli will pay EGP five million in order to complete the signing.
FilGoal.com learnt that Ahli vice-president Mahmoud Al-Khatib met with Petrojet's board members to work out the details of the deal, which is expected to go through before next season.
Petrojet, however, are yet to determine which players from Ahli to involve in the swap deal.
The Petroleum side will decide once a new coach has been appointed instead of Mokhtar Mokhtar, who announced that he will step down from his role after the ongoing Egyptian Cup.
Ahli have been eager to acquire Soliman's services for quite a while.
The prospect of joining the Egyptian champions also appeals to the 25-year-old, who is also targeted by Zamalek.
Ahli have been on the lookout for new signings in order to bolster their frontline as prolific striker Emad Meteb, who's currently nursing a back injury, could well be leaving the club in the immediate future.
Francis Doe, who joined Ahli last summer, barely delivered the goods upfront over the past months while outcasts Hani Al-Egeizi and Ahmed Belal struggled in vain to hit peak form.