The Ghanaian, who joined Die Nullfunfer during the recent transfer window, has had to wait longer for his first appearance as an infection ruled him out of Saturday's 2-1 triumph over Augsburg.
He transferred to the German outfit from Slovenian champions NK Olimpija in a five-year deal.
Having resumed training, Abass is on course to make his Mainz debut in Sunday's away trip to Bayer 04 Leverkusen.
He would hope to continue from where he left off at Olimpija
In Slovakia, the 19-year-old made 53 competitive appearances for The Dragons, netting 17 times.
His goals included three strikes in four outings in the Europa League this season.
The former Ghana under-17 attacker played for lower tier side Asokwa Deportivo during his time in his homeland.