Nigeria has been facing goalkeeping crisis after their choice keeper, Carl Ikeme was diagnosed with acute leukaemia last year.
The development sparked calls for Enyeama, who has since been dropped from the senior team of Lille, to come out of international retirement.
Rohr has, however, kept faith with young Deportivo La Coruna keeper, Francis Uzoho, Enyimba star Ikechukwu Ezenwa and much- vilified Chippa United custodian Daniel Akpeyi.
Pinnick told ScoreNigeria that Rohr would decide if he wants Enyeama.
He said, “All the other goalkeepers deserve to be in posts (for the World Cup), (Francis) Uzoho, for one, is doing well.
“This could well be the big break for one of the other goalkeepers.
“But in the end, it’s Rohr’s call to invite Enyeama, it’s his own responsibility.”
Pinnick added that goalkeeping trainer, Alloy Agu would be in South Africa to train Akpeyi.
“Alloy Agu is on his way to train Akpeyi at Chippa United.
“The other trainer (Pionetti) is in Spain with Uzoho on special permission of his club.
“We also expect such for Dele Alampasu and Ezenwa.”