The 20-year-old attacking midfielder has been one of Ajax's stand-out performers over the past few years, prompting admiring glances from a number of clubs across Europe.
Reds boss Brendan Rodgers has been credited with an interest in bringing the Eredivisie ace to Anfield, as he looks to add further creativity to his Merseyside ranks in January.
However, Liverpool's hopes of landing Eriksen have been dealt a significant blow after Italian newspaper Corriere dello Sport reported that Serie A giants Milan sent scouts to watch him in Champions League action against Manchester City last night.
Eriksen scored, and turned in another impressive display against the reigning Premier League champions, which will likely encourage AC to make a bid in the New Year.
Liverpool will hope that the offer of first-team football in England's top-flight will be enough to convince him to turn down advances from Italy, but if Ajax progress to the Champions League last-16, then he could yet prefer to stay at the Amsterdam Arena.