The 24-year-old has been with the Egyptian Premier League since 2016 when he joined the side Tunisian club CS Sfaxien.
The attacker has been delivering consistent performances for the Red Devils and in the current campaign, he has bagged nine goals amid other dazzling displays.
The centre-forward recently helped the Cairo International Stadium outfit reach the final of the Caf Champions League.
Rohr recently released a 24-man squad that will play Sierra Leone in an Africa Cup of Nations qualifying game in November and omitted the forward.
"I believe that Ajayi deserves to be given an opportunity like every other player and then it is up to him to take the opportunity," Amunike told ESPN.
"He has been with Ahly for many years now and he has been doing very well and playing at a high level consistently. I think that looking at what he has done with the Ahly club, he deserves to be given the opportunity.
"It will now be up to him to make a statement that will convince the technical staff that he has something to add to the team."
Former Nigeria international Jonathan Akpoborie also backed Amuneke’s suggestion for Ajayi to be invited to the Super Eagles, highlighting some of his attributes.
"Ajayi deserves the Nigerian shirt. Compared to most of the strikers I have seen so far for Nigeria. He scores and can create chances for his fellow players,” Akpoborie said.
"He is fast and he is an all-round striker that scores goals from inside and outside the box. He will be a valuable asset for the Nigerian team."
Ajayi is yet to make a competitive appearance for the Nigeria national team but has featured in a friendly.
The centre-forward has scored 28 goals for Al Ahly in more than 90 appearances across all competitions.