Vasseur's claim comes after Renault announced that current Force India driver Hulkenberg will drive for the French works team in 2017 and beyond.
"We believe Nico is among the best of the new generation of drivers," Renault chief Vasseur told 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."
TV2, a Danish broadcaster, claims that Magnussen's advisor Jesper Carlsen travelled to England late last week for talks with Hulkenberg's current team, Force India.
Palmer told Germany's Auto Motor und Sport: "I still have a chance to stay with Renault."
That could be because Renault's reported first choice to be Hulkenberg's teammate, Valtteri Bottas, now appears poised to in fact stay with Williams.
Also strongly linked with Renault is Esteban Ocon.
Vasseur told the French daily L'Equipe that Renault wants to sign two 'number 1' drivers.
"It works for Mercedes," he said. "I don't like when a team has one top driver and a second in the shade.
"Ocon? He's on our shortlist, it's no secret. But we need a couple of races now to look over the candidates before making a decision.
"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."
He told Infosport Plus that the decision will take "a few days or weeks at the most".
Renault have picked up eight points in the 2016 championship.