Last summer, Anderlecht expressed interest in the Dane but did not make a formal offer.
However, with Eriksen coming off contract in June, Anderlecht spy a Bosman chance for the midfielder.
Leander Dendoncker is on-loan at Anderlecht from Aston Villa and Anderlecht see Eriksen as a more affordable alternative, says Ekstra Bladet.
Former club Ajax are also watching developments closely.