Lingard - strongly linked with Newcastle United and West Ham United - was widely expected to leave the Red Devils on loan during the winter window, but the deadline passed with the England international still at the club.
Rangnick has conceded that Greenwood's club suspension contributed to Lingard remaining at Old Trafford, although the playmaker will not be involved against Middlesbrough in the FA Cup on Friday, having been given time off to "clear up his mind" following the breakdown of a proposed exit.
"Three weeks ago, Jesse didn't want to leave. Then he changed his mind. I had a chat with him 10 days ago and I could fully understand why he wanted to leave, to get game-time for his future and the World Cup. And I said to him at the time if he finds a club he would like to play for and the club find a solution with our club I would let him go and allow him to leave," Rangnick told reporters.
"Obviously, with all the developments in the last couple of days, things changed a little bit. On the other hand, we also had no agreement with any other club and we had to take a final decision with the board, and we decided to rather keep Jesse until the end of the season.
"In a way, yes, but in the end, the club told me, the board told me, they couldn't find an agreement with any of those clubs that were interested in him. With the window closing on Monday evening, in the afternoon the board informed me they would rather he stay, and this was a decision I could fully understand and accept.
"So it was two things: we had a problem with Mason Greenwood and being without a player for the time being who has played regularly in the last couple of weeks and the club not finding an agreement with another club.
"Jesse asked me and the club if we could give him a couple of days off just to clear up his mind. He will be back in the group next Monday, back for training and then be part of the regular squad again."
Greenwood was arrested on suspicion of rape, sexual assault, threats to kill and assault of his girlfriend following posts, including images and a voice note, on social media, but he has since been released on bail. body check tags ::