The Ghana international, who led the Pro League with 19 goals in the past season, remains in his home country but is expected in the UAE in the next few days to formalise his status with the 10-time champions.
"An announcement is imminent," Carlo Nohra said on Sunday.
"We always have been positive about this happening.
"We've done our homework, everything has lined up, and now we need to get everyone around a table to get a signature on the dotted line so he can travel with the team."
Gyan recently told the BBC, in Accra, that he is "thinking only of Al Ain".
"We are still in negotiations so, hopefully, I might stay at Al Ain," Gyan said. "I have done a great job. Definitely, people will like me to stay.
"Personally, I am also happy over there."
Gyan is 27, and Nohra suggested the striker is young enough that the club might investigate signing him for "three or four years".
In April, the club revealed they had invoked a clause in a loan arrangement with the English club Sunderland to negotiate a contract with Gyan, but talks with the player have never reached a formal stage and he could not have been signed earlier than Sunday.
His deal with Sunderland expired on June 30.
Nohra said that Al Ain are still seeking a replacement for the Argentine forward Ignacio Scocco, and perhaps also for the Saudi striker Yasser Al Qahtani, who had come on loan from the Riyadh club Al Hilal.
"The situation with Yasser is still quite uncertain," Nohra said.
Mirel Radoi, the Romanian midfielder, is set to return to the club, and Gyan would be the second foreigner to sign with the club for the coming season.
That leaves openings for two more players, one of whom would have to carry a passport from an Asian Football Confederation country.
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