Powell was reported to be among those in contention to replace the ousted Mike Newell at Blundell Park.
She has held her national post since 1998 and led her side to the final of the 2009 European Championships this summer.
No woman has ever managed a professional men's football team in Britain, but the League Managers' Association had vowed to support Powell had she moved for the Grimsby job.
However, she appears to be out of the running as Fenty has heard nothing from her.
"I have never spoken to the lady," he said. "She hasn't put an application in so we can hardly consider her."
Former Grimsby full-back John McDermott and ex-Hull City striker Dean Windass have expressed an interest in the job.