Song, who is on loan at the Hammers from Barcelona, has made just eight appearances this season and it is looking increasingly unlikely the club will hand him a permanent deal in the summer.
Therefore Slaven Bilic could be on the lookout for a new defensive midfielder when the club moves into its new Olympic Stadium home.
The 25-year-old Norway international is a defensive midfielder with Champions League experience and has been earning rave reviews for his performances this season.
Compatriot could swing it in West Ham's favour
One thing which could sway any potential move in West Ham's favour is the fact Nordtveit's fellow Norwegian midfielder Martin Samuelsen looks set for a very bright future in East London.
Samuelsen, who signed for the Hammers from Manchester City last summer, has been sent out on loan to Peterborough United this season to gain vital experience.
His performances have been so good many fans and pundits have suggested the club will not be able to hold him back anymore and expect to see him competing for a first team spot next season.
At 6ft 2in Nordtveit is a real athlete and would be able to cope fine with the rigours of the Premier League. There is also the added bonus that he can play at centre half, something the Hammers regularly utilise in Cheikhou Kouyate.
The Bundesliga star only has six months left on his contract and would be quite a coup for the club on a free transfer.
Available on a free transfer at the end of the campaign, Nordtveit can also play as a centre-half, offering versatility to both Premier League sides.