The club from southeastern city Aba will be happy at being paired Rwandan club Rayon Sports in the quarter-finals.
Rayon appear the weakest of the eight survivors in the African equivalent of the UEFA Europa League and it would be surprising if Enyimba did not win the two-leg tie.
Rayon host the first leg in Kigali on September 16 with the return match seven days later at a renovated Aba stadium.
However, if twice African champions Enyimba progress, they are likely to meet title favourites Raja Casablanca of Morocco in the semi-finals during October.
Raja have won six and drawn three of 10 CAF matches this season, scored 24 goals and boast the leading individual scorer in 10-goal Mahmoud Benhalib.
In the quarter-finals, the Moroccans face CARA of Congo Brazzaville, who reached the last eight after winning all six home matches but losing all six on the road.
Al Masry of Egypt face USM Alger of Algeria and V Club of the Democratic Republic of Congo meet Renaissance Berkane of Morocco in the other quarter-finals.
The draw raised the possibility of an all-Moroccan title decider between Raja and Berkane during November and December.
Hearts of Oak beat Asante Kotoko on penalties in an all-Ghana first final 14 years ago and CS Sfaxien edged Etoile Sahel on away goals in an all-Tunisia 2008 title decider.
Rayon Sports (RWA) v Enyimba (NGR)
CARA (CGO) v Raja Casablanca (MAR)
Al Masry (EGY) v USM Alger (ALG)
V Club (COD) v Renaissance Berkane (MAR)
First legs: Sept 16, second: Sept 23
Rayon or Enyimba v CARA or Raja
Masry or USM v V Club or Berkane
First legs: Oct 3, second: Oct 24
Rayon, Enyimba, CARA or Raja v Masry, USM, V Club or Berkane
First leg: Nov 23-25, second: Nov 30-Dec 2
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