The former Swansea manager, and brother of former Rangers winger Brian, is understood to have been the subject of an early approach which would also see Morten Wieghorst return to Parkhead as his assistant.
Laudrup has a strong managerial pedigree having managed Brondby, Getafe Spartak Moscow and Mallorca.
He led Swansea to victory in the League Cup in his first season in charge however he dismissed in February following a poor run of form.
Laudrup joins a long list of managerial candidates including David Moyes, Owen Coyle and Malky Mackay however it is the Dane’s commitment to attacking football which is understood to have attracted the Parkhead board.
Weighorst played for Celtic under Tommy Burns and Martin O’Neill and was a popular player at the club.
His career, however, was cut short by illness when he returned to Denmark to play for Brondby.
Celtic could face competition for Laudrup with Grenada reported to have offered him a contract to manage the national side with Southampton also believed to be interested.