Rangnick has confirmed that he gave Lingard the green light to leave Old Trafford in January, providing that the club received a suitable offer.
However, with just hours remaining of the transfer window, United told the England international that he would be remaining at the club for the rest of the season.
In a press conference on Thursday, Rangnick revealed that Lingard would not be involved against Middlesbrough in the FA Cup, suggesting that the 29-year-old had requested a couple of days off "to clear his head".
Later in the day, Lingard refuted those comments, taking to Twitter to say: "The club advised me to have time off due to personal reasons! But my headspace is clear and I'll always be professional when called upon and give 100%."
Lingard, who has five months remaining on his contract, had been heavily linked with a switch to either Newcastle United or West Ham United.
He has been restricted to just 89 minutes of Premier League football this season, his nine appearances coming from the substitutes' bench. body check tags ::