The Dutch fired coach Danny Blind after a 2-0 defeat to Bulgaria, with the Oranje six points adrift of France in their World Cup qualifying group and in real danger of missing out on Russia 2018.
Koeman only moved from Southampton to the Toffees last summer, while other names touted are Frank de Boer, Guus Hiddink and Dick Advocaat.
The Dutch FA want to stamp out the current malaise, which saw them fail to qualify for Euro 2016, and have said they want to appoint “many experts”, with local reports claiming former Manchester United manager Van Gaal is in the frame.
"For the profile we're looking for we have a technical director, but we will also look for many other experts," football director Jean Paul Decossaux told De Telegraaf.
Read the full article on eurosport.co.uk: Dutch mention Koeman for manager job, LVG could be adviser