In the 24 hours before close of business on Thursday, it was widely reported that the respective teams had reached an agreement, a loan with a £15m obligation.
With Benrahma having been seen in France, West Ham manager David Moyes acknowledged on Thursday night that he assumed that the transfer would go through as planned.
However, the deal was not processed by 10pm - the transfer deadline in France - and it was subsequently reported that the transfer had collapsed.
That was soon confirmed by a West Ham spokesperson, but Lyon reacted by launching an official statement, describing West Ham's actions as "incomprehensible".
It read: "Olympique Lyonnais were delighted to welcome Said Benrahma to Lyon this Thursday to finalize his transfer from West Ham. The two clubs had signed a temporary transfer agreement, and Olympique Lyonnais had obtained approval from the DNCG to allow the transfer to take place smoothly and transparently.
"However, at the start of the evening, while Olympique Lyonnais had entered all the administrative data on the dedicated FIFA platform (FIFA TMS), West Ham had never launched the slightest technical procedure on its part, despite the repeated reminders from the OL and continuous mutual telephone communication.
"In the absence of this reciprocal action on the part of the English club and following this incomprehensible behaviour, raising questions, the international transfer certificate could not be requested before closing time.
"Olympique Lyonnais deeply regrets this situation and this decision, demonstrating a profound lack of respect on the part of West Ham towards the institution and the player.
"The club reserves the right to initiate all appropriate procedures necessary to validate the transaction at a later date, and to hold West Ham responsible if necessary."
As well as the exit of Benrahma not materialising, the expected transfer of Pablo Fornals to Real Betis has also not been confirmed by West Ham.
Transfer expert Fabrizio Romano says that the Spanish outfit 'hope to get the green light' to conclude that particular deal in due course.
West Ham had been hoping to strengthen their squad on Thursday, but they allegedly failed to secure a deal for Marseille winger Ismaila Sarr.