Keen on reaching an agreement with Al Ahly, the French club submitted an improved offer of $3.5 million, but was again rejected by the soon-to-be Egyptian champions who asked Nice to get closer to their valuation of $6 million.
If Abdelmonem completes a move to the French club, he will become the ninth-ever Egyptian to play in the Ligue 1 and the first to represent the Eaglets.
Nice finished last season fifth in Ligue 1 and secured Europa League football for next season and will be hoping to strengthen their squad, having lost Khéphren Thuram to Juventus earlier this summer.
The club is owned by British petrochemical giant INEOS, which also owns Swiss Super League side FC Lausanne-Sport and a 27.7% minority stake in Premier League giants Manchester United.