O’Neill is keen to bring in the Norwegian this summer, but face competition from Liverpool, Arsenal and Everton.
The 27-year-old has been a hit at Fulham this season and O’Neill wants him to replace Martin Laursen, who is set to retire in the summer due to a serious knee injury.
O’Neill told News of the World: “I’ve been checking out players all over the place.
“We’re looking at players to try and improve the team. That is the important thing. There is a lot of competition out there though.”