West Ham and Newcastle were interested in signing Lingard after Rangnick had given the midfielder his blessing to leave in January.
But, after Greenwood was arrested on suspicion of raping a woman and other offences, United blocked a late exit for Lingard, much to his dismay.
Greenwood has been suspended by United, who have said he will not return to training or play matches “until further notice”.
Speaking on Thursday, Rangnick said: “A few weeks ago Jesse did not want to leave but changed his mind. I had a chat with him some 10 days ago and could fully understand why he wanted to leave, to get game time for his future and for the World Cup.
“I said to him at the time, if he finds a club and the club finds a solution with our could, I would let him go and allow him to leave.
“But obviously with all the developments we had in the last couple of days things changed a bit. We also had no agreement with any other club.
“We had to take a final decision with the board and we decided to keep Jesse until the end of the season.”
After a a deadline-day exit blocked, Lingard will not feature against Middlesborough in the FA after being granted some time off to “clear his mind”
Rangnick said: “He asked me and the club could I give him a couple of days off just to clear up his mind. He will be in the group next Monday and then be a regular part of the squad again.”