The Nigeria Football Federation (NFF) announced Saturday that Amodu, 58, died after complaining of chest problems.
On Wednesday, Keshi, 54, died suddenly in the southern Benin City.
Amodu, four-time Super Eagles coach, also died in his sleep in the same city.
Amodu, who qualified Nigeria to two World Cups, in 2002 and 2010, was to have replaced Sunday Oliseh, who quit as the country’s coach in February, but he declined on health grounds.
The top coach was recently appointed Nigeria technical director.
Senior football officials told AFP Amodu was hypertensive and had been on medication.
Keshi assisted Amodu when Nigeria qualified for the 2002 World Cup.
Amodu rose to prominence when he guided BCC Lions of Gboko to win the Africa Cup Winners Cup in 1991.
He was subsequently rewarded with leading the Super Eagles in 1994.
He would take up this post at least three other times during which time he qualified the country to two World Cups.
But on both occasions he was not the man in charge at the final tournaments.
He also handled top South African club Orlando Pirates between 1996 and 1997.