The wrap was controversially dropped after the organising committee was asked to find £20m in savings following the Comprehensive Spending Review.
The 900m-long, 20m-high wrap was expected to cost £7m, but was a key piece of the structure's design, minimising cross-winds blowing through the stadium.
However, Paul Deighton, chief executive of the London organising committee (Locog), told the BBC that there had been "significant interest" in the project from the private. "Now is the time to start a formal tender process," he said. "There are some exciting ideas around, and we are running a process that is fair to those organisations that have expressed an interest."
Interested parties have until 18 February to register interest in supplying the wrap.
Olympic Stadium wrap project brought back after private sector interest
The body organising the London 2012 Olympics has said it is open to "expressions of interest" in tendering for a giant fabric wrap to cover the Olympic Stadium.
