The team announced Nico Hulkenberg as their first 2017 driver last week, but the identity of the person who will occupy the second seat is still unknown.
A number of drivers have been linked with the second seat including Esteban ocon and Valtteri Bottas.
"Ocon? He's on our short list, it's no secret. But we need a couple of races now to look over the candidates before making a decision," said Vasseur. "I know Bottas too and like him, and we are carefully watching him, but as far as I know, he has a contract with Williams."
The decision will take "a few days or weeks at the most," he added.
Current driver Jolyon Palmer still believes he has a chance of remaining at the team, telling Germany's Auto Motor und Sport: "I still have a chance to stay with Renault."
Meanwhile, Vasseur is looking forward to working with Hulkenberg again, having been boss of ART Grand Prix when the German drove for the team in Formula Three and GP2.
"We believe Nico is among the best of the new generation of drivers," Renault chief Vasseur told the French broadcaster Infosport Plus.
"I have worked with him in the junior series - he is one of the drivers who has won everything, from Formula BMW to F3 and GP2.
"In my opinion, Nico realises that this stage of his career is right to starting working with a factory team. Confirmation of the contract with him is an important step for our team," Vasseur added.
Bahrain International Circuit - Winter testing