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.
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".