Rangnick said after Saturday's game that Martial, who has been linked with a move away from Old Trafford this month, "didn't want to be in the squad".
Martial countered on social media, stating he would "never refuse to play a match for Man United".
The 26-year-old has not played a single minute since Rangnick took charge in November.
"I'm here now for six weeks. All the things that needed to be said, I said after the press conference," commented Rangnick ahead of United's trip to Brentford on Wednesday.
"I had a conversation with him on Sunday, a personal conversation with him about what happened and how I saw the whole situation. The matter is now resolved.
"He didn't train yesterday and the day before yesterday. He will probably train today and after training I will then take the decision if he is nominated or not (for the squad)."
Martial is highly unlikely to feature, with Cristiano Ronaldo and Marcus Rashford back in contention after returning to training.
However, it is the return of Paul Pogba that has caught Rangnick's eye.
The French World Cup winner has been sidelined by a thigh injury since early November, but returned to training on Monday.
"Paul Pogba had his first day of training with the whole group yesterday and in the first training session he showed what kind of an extraordinary player he could be," said Rangnick.
Pogba could be nearing the end of his second spell at the club, with his contract expiring at the end of the season, but Rangnick said he was not dealing with the issue personally.
"I'm not negotiating about future contracts with players," said the German, who is set to remain at United for the next two years in an advisory role once his interim spell in charge finishes after the current campaign.
"But what you could see from his very first day in training is that he's present -- he's physically present and mentally present.
"What I saw in training yesterday was very promising for the future and I'm very much looking forward to having him available in two weeks' time after the international break. I think he will be a serious candidate also for the first 11."
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