The telegraph reported that the group, which began a strategic review with adviser UBS in March, said it had received a number of offers for the business, worth around £85m, and is now in the final stages of a sale with one potential buyer.
Pipex already sold its broadband business to Tiscali for £210m last September and has used the cash to wipe out £90m of debt.
Should the sale of its hosting and networking business go through, Pipex plans to add the proceeds to the remains of those from the broadband sale, and return the capital to shareholders, after clearing possible further debts.
The group's fledgling wireless unit would be all that is left of Pipex, and would represent a fundamental change to the business under the rules of the Alternative Investment Market - forcing it change its name and seek shareholder approval for the deal.
The wireless business owns licences to offer broadband services using the long-distance technology known as WiMax. It already operates under the name FREEDOM4, a joint venture between Pipex Communications and Intel Capital.
Pipex told shareholders that should they approve the sale of the hosting and networking arm at a general meeting in March, the group would rename itself FREEDOM4 Communications.