Tata is selling its entire loss-making UK business and has asked for expressions of interest as part of the sales negotiations process.
Mr Wilkie was one of the main people behind a survival plan that was rejected by the Tata board in India and the UK business was put up for sale.
The steel crisis has been driven by falling prices and a global oversupply.
In the UK, high energy costs and cheaper Chinese imports have exacerbated the issue.
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The steel union Community said it would welcome "prompt discussions with Stuart Wilkie and any management buyout option".
BBC Wales business correspondent Brian Meechan said that, as with any potential buyer for Tata, the management buyout would require significant financial support from the UK government.
"It's believed though that any management buyout would involve retaining the blast furnaces and making steel from scratch as opposed to the proposal by Liberty to turn it into a recycling facility," he added.
Tata Steel directly employs 15,000 workers in the UK and supports thousands of others, across plants in Port Talbot, Rotherham, Corby and Shotton.
The company has sold its Long Products Europe business at the Scunthorpe plant, safeguarding 4,400 UK jobs, but workers are being asked to accept a pay cut and less generous pension arrangements.
The government has resisted calls from unions and opposition politicians to nationalise the Port Talbot plant, Britain's biggest steelworks, to safeguard thousands of jobs.
Steel company Liberty House, owned by Sanjeev Gupta, has publicly expressed an interest in buying the Port Talbot works.
Tata Steel's Port Talbot chief Stuart Wilkie is to launch a management buyout of the company's operations in the UK.