Names like Simeone, Gallardo and Gareca have all been linked and in the last few hours Manchester City's Pep Guardiola has been added to the list.
According to various reports, the Argentine Football Association (AFA) have looked into the possibility of offering the coach a huge contract to take over from Sampaoli.
However, before that, they must resolve Sampaol's situation. The former Sevilla coach would need to be paid off a large sum of money if he was sacked.
A while ago, Guardiola showed an interest in one day coaching Argentina, where he would be reunited with Lionel Messi, who he coached while at Barça, and a number of his City player, like Sergio Aguero and Nicolas Otamendi.
The main obstacle, though, is the fact that Guardiola recently renewed his deal at the Premier League champions until 2021 and it doesn't look like he's about to follow Julen Lopetegui's lead.
In any case, the rumours have started