The 25-year-old Sierra Leone international has been playing in Norway since 2006, after he saw a move to Watford fall through when he was not granted a work-permit.
Bangura had initially impressed Watford at the World Under-17 World Cup, but after seeing his move to Vicarage Road collapse - they still owned him and he was loaned to Honefoss.
After his deal with Watford expired in 2008, he stayed with Honefoss before then in 2010, joining Haugesund.
Now after emerging as one of the best defenders in Scandinavia, Palace have made their move to land Bangura - whose current deal is due to expire at the end of this year.
It is understood that an opening bid from Palace has already been rejected by Haugesund, something Bangura is far from happy about.
"I am very disappointed," he is quoted by Haugesund Avis.
"I'm ready for new challenges, and the Premier League is a great opportunity for me and Crystal Palace want me now.
"I only have a few months left on my contract before I can go for free, so the choice should not be that difficult."
Because Sierra Leone are now ranked in Fifa's top-70 - Bangura, who is a regular for his country, would qualify for a work-permit to play in England.