Martial has appeared in 10 games this season, scoring one goal.
Anthony Martial told the Manchester United interim manager he wanted to leave.
He said the man told him it was the right time for a change.
Martial has scored once this season.
Despite his desire to leave, the club had not yet received an offer for the forward.
Martial wanted to leave the club in January, according to his agent, who said he would speak to the club soon.
He explained to me that he feels it's the right time for a change, since he's been at Manchester United for seven years.
Martial was the world's most expensive teenage footballer when he joined United from Monaco in 2015.
He has scored goals in 268 appearances for Manchester United, but has become a fringe player since the arrivals of Edinson Cavani, Jadon Sancho, and the likes of CristianoRonaldo.
He has made just 10 appearances this season and has not been involved in any of the games in charge.
"I think it's understandable," said Rangnick.
It's important to see the situation of the club, but I could follow his thoughts. We have high ambitions and want to be as successful as we can be, which is why we have three competitions.
"So far, as far as I know, there has been no offer from any other club and as long as this is the case, he will stay."
Vaccine status could be a factor for new signings.
He said that he shares the concerns of the manager over signing players who are not protected against coronaviruses.
The club's decision to sign a player would be influenced by their vaccine status.
"I think it could be a consideration," he said.
The clubs have to think about this. If you sign a player who isn't up to date with his vaccinations, you have to be aware that he might not be available.
This could happen frequently in Covid times.
The first-team section of United's facility was shut down due to the Covid outbreak and two games were postponed in December.
According to recent figures, the league said that 84% of players are on their journey to be vaccine free.
The figures are in line with other age groups.
The example of Joshua Kimmich was used by Rangnick as proof that players should get vaccinations as soon as possible.
The Germany international, 26, recently said he regrets not being vaccined after he had a lung problem.
Kimmich was hesitant at the beginning, but I think he has realized it might be a good idea to get vaccine.
He has some problems with his lungs after catching Covid. I think this is an issue where everyone can have his free will. We need to convince our players to get vaccinations in football, especially at this level.
It should be in the best interest of the players to be vaccine free, but it's a decision that each club has to make.
Should sport be tough on vaccine hesitancy?