Digne is one of the hottest prospects in French football and has also been linked with a move to Spain or Italy at the end of the season.
Lille are currently struggling to qualify for Europe in the French league and so Digne may be tempted away with the prospect of Champions League football.
The 19 year old could be seen as the long term replacement for fellow Frenchman Patrice Evra at Old Trafford despite the Premier League leaders signing Alexander Buttner in the summer.
Sir Alex Ferguson is focussing on bringing youngsters into his Manchester United squad to join the likes of Wilfried Zaha and Danny Welbeck with players such a Paul Scholes, Ryan GIggs and Rio Ferdinand coming to the end of their careers.
“Manchester United: They are a top club and to be linked with them means you must be doing something well, but I will not lose sleep,” Digne told Le 10 Sport:
“I live day to day because I feel very happy at Lille, this is the club of my heart, the club that developed me.
“I do not make plans in a rush. I am very much at Lille, I am not planning to leave.