The German tactician led the Eagles to a third-place finish in the just concluded 2019 Africa Cup of Nations after they missed the last two editions.
Rohr had come under heavy criticisms from several directions for what some described as “lack of tactical nous” or “inability to read matches”.
Reports say the 66-year-old has informed close associates that it was unsure if he would continue with the job.
Sources told ESPN: “A lot of things have been going on but he has taken it all because he does not want to cause any controversy.
“But now, he is not sure if he will continue.”
Rohr is due to face Amaju Pinnick, President of Nigeria Football Federation, this week as part of that assessment.
And if both parties reach an agreement, he might leave the role sooner than expected.