The Championship outfit confirmed at the end of last month that they had entered into a period of exclusivity with Turkish television mogul, who has been speaking to the Allam family about taking over for some time, having first visited the club in May.
Delivering a message on Twitter and also posting a video of his visit to Hull in the Spring, Ilıcalı said: "I hope this process will be completed soon and that my dream turns into a reality.
"I am also blown away by their great support in the away games.
"Ehab Allam is an exceptional person and was a huge help to us during this period. I would like to extend my deep gratitude and respect to him and his family."
Hull have been on the market since 2014 with the Allam family having been keen to sell up for a number of years, having bought the club back in 2011.
Recent reports in the Turkish media said a £30m price had been agreed, with a further £20m due if the club reach the Premier League, although the reports did not put a timeframe on this.
City headed into the latest international break on the back of an encouraging 2-0 victory at Barnsley, which ended a run of five successive defeats.
They remain in the Championship relegation zone and are three points adrift of Peterborough United.
Hull welcome Birmingham City in their return to action on Saturday week.