Faroe Islands are bottom of the group- which is led by Spain who have a maximum of 18 points. With 4 matches left, the Faroes have lost all 6 of their games.
"8 years is a long time in football. The results haven't been good recently either. I also think the federation wants new eyes to take the next step", Olsen said at a press conference in Torshavn, the capital of the Danish territory where only 50,000 people live.
They are still to welcome Romania and Malta, and play away to Norway and Sweden- the two teams that are vying for 2nd spot with Romania.
Faroe Islands, who have never played at a major tournament, have achieved some of their best results during Olsen's time in charge, above all in the qualification campaign for France 2016 where they got a record 9 points and beat Greece twice.
The 58-year-old has managed several clubs such as Brondby, Randers, and OB, although he is more remembered as a player. Olsen played 84 times for his country and was the captain when they surprisingly won Euro 92.