The 28-year-old has been the subject of two bids from the Middle Eastern side and a third, improved offer was received by Hibs ahead of the Scottish Cup fourth-round tie against Cove Rangers.
Boyle was left out of the squad and watched the game from the stand, but appears to have played his last game in green and white.
Speaking afterwards Maloney said: “I was always aware this could happen but in terms of Martin as a person he's been great to deal with.
"We've been really clear with what the situation could be; it ended up changing a little bit before the game and I think we could know more in the next 24-48 hours.
“In these games players like Martin make a difference, and he was missed tonight.”
Admitting that, in the event of Boyle’s departure, Hibs would face an uphill battle to source a like-for-like replacement, the Hibs boss added: “Players like Martin are hard to find – that's why he's been one of the best players in the league in his position.
“But we can't not replace him. Even at times against Cove, we had some good play but if we had a player with Martin's attributes then it could change a really long possession into a big chance.”
However, Maloney played down talk linking Hibs with a move for former Hearts loanee Demetri Mitchell, adding: “He's still a Blackpool player so I wouldn't want to speak about that just yet.”