According to Het Laatste Nieuws the 25-year-old Argentine international has been identified as a replacement for Darren Fletcher, who announced yesterday he will take some time away from the game.
Red Devils boss Sir Alex Ferguson was already believed to be considering recruiting a new midfielder when the transfer window reopens in January, and news of Fletcher's injury now means the club will almost certainly add to their Old Trafford ranks in the New Year.
However, Manchester United may face competition from Gunners boss Arsene Wenger - who is also weighing up an attempt to bring Biglia to the Emirates Stadium.
Arsenal signed Mikel Arteta on transfer deadline day in August, but having sold Cesc Fabregas and Samir Nasri in the summer, Wenger could move for another midfielder in January.
The South American star is rated at around €7million - a price tag that is well within both Arsenal and Manchester United's respective budgets - and although Biglia is under contract at Anderlecht until 2015, he could move to England before the end of the 2011-12 campaign.