The 19-year-old is highly rated in Europe as a result of his performances in Holland, and according to reports in talkSPORT, has attracted the attention of Liverpool manager Kenny Dalglish.
The savvy Scot already had his eye on the young star earlier this summer, but a deal failed to happen.
However, the Merseyside club will now be pushed to act fast, as AC Milan have also entered the race to snap up Eriksen.
The Serie A big-spenders are keen to bring him to the San Siro to bolster their attack, but both clubs will have to persuade Ajax to do business in the first place, as the Dutch club were closed to doing business during the summer.
That could change in 2012, as clubs look to bolster their sides in the January transfer window, and a bidding war could well erupt for Eriksen then.