The former Kalmar defender has linked up with the Hammers in recent weeks, and manager Sam Allardyce is seemingly keen to take an extended look at the centre back.
Given that he's far from a household name in English football, so here are five things West Ham fans need to know about their trialist...
- Nilsson, now 26, was a regular for the Sweden youth sides, making 32 appearances at Under-17, Under-19 and Under-21 levels.
- Despite being highly regarded in his early years, Nilsson has just one cap for the Swedish national team, making his debut in 2011 against South Africa.
- Nilsson stands at 6ft 4in tall, and is a huge, imposing centre back with great strength and aerial ability - attributes that will be appealing to Sam Allardyce.
- The defender has spent almost all of his career in Sweden, playing for Helsingborgs and Kalmar, returning to his homeland after a tough three year spell with Utrecht in the Netherlands.
- After leaving Kalmar last month, Nilsson is a free agent and would be able to sign for West Ham on a free transfer should Sam Allardyce wish to keep him at Upton Park permanently.