The former league champions have told the two technical crew members to leave their duty posts because of poor results after two consecutive losses
The decision to suspend both coaches Goal gathered was a result of their two consecutive losses in the Nigeria Professional Football League including a shock 0-1 loss to city rivals, Abia Warriors at home.
Baraje has only been in charge of the People's Elephant for four months as he assumed the head coach role in December.
The former Dolphins coach has only taken charge of seven official games in the Caf Champions League and NPFL this season and has won three, lost three and drew one.
But Enyimba are still to make an official announcement on the decision to axe their head coach and his assistant as they prepare to make the trip to Warri Wolves.
"Coaches Baraje and Monday Odigie won't be part of the technical crew in our next match. They have been suspended by the club indefinitely but no official word yet. The move is because the team failed to win at FC Taraba, and even played poorly. The team has struggled to impress since the season started.
"Remember the team lost at home to Abia Warriors and after that game, the club management handed them the ultimatum to win at FC Taraba or face the consequence which is what has now happened," said a top Enyimba official to Goal on Monday.
Our attempt to speak to Enyimba chairman, Felix Anyansi Agwu was declined. "I'm unavailable to grant interviews now," Anyansi Agwu said.
Enyimba have now travelled straight to Warri from Taraba without Baraje and Odigie among their contingent, leaving another assist coach, Imama Amapakabo, to take charge of their match day plans against Wolves this Wednesday.
Indications became stronger about the suspension of the two coaches when Enyimba's official website quoted Amapakabo as talking about the match against Wolves.
"Our next game against Warri Wolves is one we will take with a lot of seriousness before returning to Aba to get to work on the flaws of the team," Enyimba's caretaker coach, Amapakabo said to Enyimbafc.net.
In March, Enyimba suspend their goalkeeping coach, Shuaibu Suleiman, after they lost at home to AS Real de Bamako in a Caf Champions League match.
Enyimba currently occupy 14th position in the NPFL standings after taking just four points from four matches.