Ntcham was brought in from the Scottish champions on the last day of the winter transfer window on a deal that lasts until the end of the season, with Marseille having the option to sign him permanently if he impresses.
But Villas-Boas insists he did not sanction the move and will gladly leave his post if the club approves.
It has been a bad few weeks for Marseille, who have lost their last three league games and got their Ligue 1 match against Rennes last weekend called off after the club’s fans attacked their training ground.
"It's a decision that was not made by me. This is a player I said no to," the 43-year-old former Chelsea and Tottenham Hotspur manager told a press conference ahead of Wednesday’s game at Lens.
"I was not aware of it, I learned of the signing when I woke up and went on the number one Marseille website. I submitted my resignation saying that I didn't agree with the sports policy.
"The board has not yet given me feedback. I do not want money, I just want to leave. This club has already experienced two or three years of randomness in terms of its transfers and I cannot accept that."
"Now I am focused on Lens. For me, they are the team of the year. We are not going to be able to prepare in the best conditions," he added.
"And I will continue until such time that the board asks me to leave. This has nothing to do with the incidents that occurred on the weekend.
Villas-Boas was appointed Marseille manager in the summer of 2019 and led the club to a second placed finish in his first season, qualifying for the Champions League in the process.
The Stade Velodrome outfit have had a more difficult season this time round and are ninth on the table, having also finished bottom of their Champions League group.
