The Sunday Mirror reports that Liverpool boss Brendan Rodgers is keen to sign the duo in a £22million deal.
Both Eriksen and Alderweireld have just one year left on their current deals with Dutch side Ajax.
The duo is expected to leave Ajax this summer and have been linked with Europe’s top clubs.
Ajax coach Frank de Boer said: “I would want nothing more than having Christian with us for a few more years.
“But we realise that the interest in this kind of player is huge. And I can also understand that he wants to make another step in his career. I can’t stop him.”
De Boer added: “If Liverpool go back to really good possession play, it can be a success for Christian. But it does mean that their entire way of playing has to change. It is up to Christian what he wants. If he feels good going to Liverpool anyway, then it is up to him.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.