The Argentina international, who has been linked with a number of Premier League sides including the Gunners, Newcastle and Norwich, has gone AWOL this week, with the Belgian club already reportedly lining up a replacement.
AC Milan are also thought to be keen on the 26-year-old defensive midfielder, who is contracted at Anderlecht until 2015.
Biglia, who joined the club from native side Independiente in 2006 and is thought to have an eight million euro (£6.6m) price tag, has previously spoken of his desire to join a bigger league.
Anderlecht, currently on their winter break, released a statement on their official website earlier this week when Biglia failed to report for duty in Belek.
It read: "The Anderlecht board have unsuccessfully tried to get in contact with Lucas Biglia and his agent.
"Today the club has called in the help of their lawyers to protect the rights of RSC Anderlecht."
Meanwhile, reports in Holland suggest Heracles Almelo striker Samuel Armenteros has reached an agreement with Anderlecht over a summer move.
The 22-year-old was expected to join another Eredivisie club, with Ajax, AZ Alkmaar, Vitesse Arnhem and Feyenoord all thought to be keen, but Anderlecht are thought to have won the race for his signature.
He told Dutch newspaper De Telegraaf: "Anderlecht is a fantastic club and has a coach who really wants me."