The winger departed the club last week for a reported fee of around £3million, joining Saudi Arabia club Al-Faisaly on a two-year-deal.
With a combined ten goals and assists in the league, Boyle was Hibs’ attacking talisman.
Manager Shaun Maloney has revealed the process for the Australian international’s replacement started when Al-Faisaly’s bid was progressing and it is currently “ongoing”.
“As soon as his situation became more serious the work to find those specific attributes was accelerated — but at the moment there’s nothing," he said,
“When you look at how he did for this club over the past few years, it’s difficult to replace that — but that’s our job.”
Maloney confirmed the club are willing to spend money, but will not be rushed or pressured into such a decision.
Despite Boyle’s importance to the team, the club are happy to wait until the summer window to ensure they get the right replacement.
He said: "It has to be the right profile, the right person, and if that's the case, then we will spend the money that's needed to bring that person here. It has to be the right one though.
"All the work has to be done and I have to be very happy with who that is. When I decide, then we can spend it.
"If it's this window, then brilliant. If not, we will wait until the summer.”