Everton are keen to talk to the Southampton and Ajax managers.
Everton are without a manager at present, having sacked Roberto Martinez following a disappointing campaign.
A number of names have been linked with the job already, which is a highly attractive one given the squad and funds now on offer at Goodison Park.
Recent reports have suggested that Southampton manager Koeman is their top target given the success he has enjoyed with the Saints over the last two years.
And it seems they will at least try to sit down with him to discuss a potential move, with them hoping to hold talks in the coming days.
He will not be the only one though, with former Ajax manager Frank de Boer also set for discussions about the position, according to the Daily Mail report.
He left the former Dutch champions last week and has made it clear that he would be open to a move to the Premier League.