Lazio are facing a battle to keep hold of their star defender, who is due to fall out of contract next summer and could walk away on a free transfer unless he pens a new one.
Talks over a new deal are reported to have stalled and unless the Italian outfit can reignite a deal quickly they may have to consider the option of selling when the transfer window re-opens.
De Vrij will not be short of offers and has the option of staying in Serie A. Both Italian champions Juventus and also Inter Milan are known to be keen and will make moves of their own in the new year.
However, Liverpool could offer him a fresh challenge in the Premier League and he would cost considerably less than Van Dijk, who still remains a Saints player.