The position has been left vacant since Stanley Young left NYSE for a role at Bloomberg in May, and according to the Financial Times, Robson is the favourite to replace him.
Robson became head of Thomson Reuter's new business development unit in December last year, after a shake-up of its markets business, which has been facing stiff competition from Bloomberg.
He was also chief executive and president of Moneyline Telerate from 1997 until 2003, when he agreed to sell it to Reuters for £110.96 million.