The 20-year-old has also been linked with the likes of Inter Milan and Arsenal.
The Mirror reports that Southampton boss Nigel Adkins is confident he can complete the signing of Boilesen this week.
The Saints are reportedly planning to make a £5million move for the defender.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?