McLaren chairman Ron Dennis is trying to take back control of the McLaren Group.
The 67-year-old has agreed with his fellow shareholders a price at which he could take a majority shareholding if he can raise the necessary money.
All parties will remain shareholders if the deal is finalised.
A McLaren spokesman said: "No transaction has taken place, but the shareholders have had discussions on how to best facilitate and enhance the future growth of the McLaren Group.
"When and if a transaction takes place, it is not envisioned that the current shareholders will exit McLaren completely, and announcements would be made at the appropriate time."
Dennis has not yet raised the money required to buy the shares he would need to take his holding past 50%, and the other shareholders are not obliged to sell if he does.
McLaren refused to say how much Dennis needed to raise, but the company is said to be worth about £1bn so he would require at least £250m.
BBC Sport has learned the Bahrainis want to remain involved in McLaren, contrary to speculation.
It is widely known within F1 that there has been tension at board level at McLaren in recent months following the deterioration of the relationship between Dennis and Ojjeh.
The two joined forces in McLaren in the early 1980s and have been business partners ever since.
But they have been at loggerheads recently over professional and personal issues.
Ojjeh, 62, has been back to health since the summer after surviving two double lung transplants over the winter of 2013-14.