In connection with the newly Genii Capital-controlled team, the Frenchman's name has arisen in recent days. Reports said the former boss of the GP2 team DAMS has recently been the director of the sports management firm Gravity.
Like Genii, Gravity is connected with Renault's new majority team owner Gerard Lopez.
Bob Bell is Renault's current interim boss, but Boullier is the longer-term successor to the departed Flavio Briatore, the BBC said.
He was introduced to staff at the team's Enstone base on Tuesday by Lopez, the report added.
Bell will return to his role as technical director.
"There are some discussions, but it is definitely still pending further discussion," said Boullier. "It's one possibility."