Greenwood, 20, has been released on bail following his arrest on Sunday.
He will not train or play for the club until further notice.
Rangnick said Lingard had been given a couple of days off “to clear his head” and would miss Friday’s FA Cup fourth round tie with Middlesbrough.
“He asked me and the club if we could give him a couple of days off just to clear up his mind,” said Rangnick.
However, Lingard has since said his “headspace is clear”.
“The club advised me to have time off due to personal reasons!” he wrote on Twitter.
“But my headspace is clear and I’ll always be professional when called upon and give 100%.”