The 900m-long, 20m-high wrap will be placed around the base of the East London stadium.
The proposal had been scrapped in October last year, after the government challenged the Olympic Delivery Authority to find savings of more than £20m.
However, London 2012 chairman Lord Coe revealed that brands had expressed an interest in funding the scheme. A tender for "expressions of interest" will therefore be issued later this month.
Controversially, brands that are not official Olympic sponsors will be allowed to approach Locog about bidding for the property.
In November, Absolute Radio launched a high-profile campaign to restore the wrap. The station proposed that the wrap carry 700,000 images of individual members of the public, as part of a wider competition.
Locog declined to comment on the tender.