Newcastle, West Ham — where he excelled on loan last season — and Tottenham were among the suitors for the 29-year-old, who is out of contract at the end of the season, but United decided to keep him at Old Trafford.
Rangnick revealed on Thursday that the frustrated England midfielder had been granted a short leave of absence and would miss Friday’s FA Cup fourth-round tie against Middlesbrough.
But Lingard said it was the club’s decision to grant him time away and that he was ready to play if called upon.
“The club advised me to have time off due to personal reasons!” he tweeted.
“But my headspace is clear and I’ll always be professional when called upon and give 100 percent.”
Lingard’s rebuttal comes after Anthony Martial — now on loan at Sevilla — last month contracted Rangnick’s claim he refused to be in a match squad, saying he would “never disrespect the club”.
Rangnick said the situation regarding Mason Greenwood was partly behind the decision to keep Lingard for the rest of the campaign.
Greenwood, who was arrested on Sunday on suspicion of the rape and assault of a woman, has been released on bail pending further investigation and remains suspended by United.
Rangnick likened Lingard’s situation to that of Paul Pogba, whom the interim boss has previously suggested could be motivated by the chance to earn a new deal elsewhere.
The France World Cup winner, 28, who is also out of contract at the end of the season, is set to return to action on Friday after three-month lay-off with a thigh injury.
“It’s up to him now,” Rangnick said. “His contract is expiring in the summer and no matter if in the end he would like to stay or go somewhere else, he has to show up.
“It’s not only in the interest of us as a club, also in his personal interest that he plays and performs on the highest possible level in the next couple of weeks.”
Rangnick, who is due to start a two-year consultancy role with United after finishing his interim stint at the end of the current campaign, did not offer clarity on Pogba’s future.
Asked if he was recommending or even urging the club to sort out a new deal with Pogba, he said: “We haven’t spoken about that at all so far — not only about Paul’s situation but also about other players with contracts expiring in the summer. We also didn’t speak about new players so far.”