The out-of-favour Manchester United man is said to be a target for struggling Crystal Palace.
Palace are without regular left-back Pape Souare for some time after the Senegalese was injured in a car accident earlier this year.
The report claims that while other clubs have also shown an interest in the England international, he has no intention of leaving Old Trafford this winter.
Palace have been playing natural right-sider Martin Kelly in Souare's absence, with former United man Zeki Fryers their only other recognised left-back.
Shaw, who has appeared 12 times this season in all competitions, is likely to earn a recall for the Red Devils' EFL Cup tie against West Ham United on Wednesday evening.
The 21-year-old cost United a reported £30 million from Southampton in 2014, but struggled in his first season and spent much of the 2015-16 campaign sidelined through injury.
Palace welcome Jose Mourinho's men to Selhurst Park in two weeks' time.