The newest name on the Everton short list today is FC Braga manager Paulo Fonseca. According to reports from ESPN, Everton had people at the Portuguese Cup final to view the manager's side defeat Porto.
Fonseca is considered an up-and-coming managerial talent in Portugal, but still carries the stigma of his poor results in one season with FC Porto, where he sacked in March 2014.
While only 43 years old Fonseca has managed at quite a few teams including two stops with Pacos Ferreira either side of his spell at Porto.
He has rebuilt his reputation though after that short stay at Porto and now appears to have gotten the attention of a Premier League side.
Everton would have been impressed with his Portugal Cup win, but also a fourth place finish in that league and a quarterfinals appearance in the Europa League.
The win was Braga's first in the cup in 50 years and made Fonseca quite popular with the fans. It might be a tough sell to Braga to release Fonseca from his current contract, but if he has ambitions to manage in the Premier League this would be a great opportunity for him.
There are rumors that Fonseca is not the only Portuguese manager on the Everton list as Andre Villas-Boas is under consideration as well.