The Saudi Arabian outfit had an offer for £500,000 turned down last month, but last week increased their bid to £2m in the hope that would tempt Easter Road supremo Ron Gordon into selling the 28 year-old.
However Hibs value Boyle significantly higher and on Monday morning told Al Faisaly that they would need to enhance their proposal.
The Scotsman understands that Al Faisaly are not prepared to pay any more than £2m for Boyle and have now moved on to another target in the forward area.
Hibs have been braced for interest in Boyle this transfer window, with his performances for Australia catching the eyes of many teams in the Middle East.
These clubs can dramatically increase Boyle’s salary, with Al Faisaly willing to pay Boyle £1m per year.
But Boyle is content in Edinburgh and Hibs are now hopeful that they can get to the end of the month with their player still at the club.
Celtic have also been linked with a move for Boyle who has scored 11 goals for Hibs this season.
Boyle signed a new contract with the club in the summer, which keeps him at Easter Road until June 2024.