Song, 27, still has two years remaining on his Barca contract and is reportedly valued at around £5million.
The Hammers are keen on landing the former Arsenal midfielder on a permanent basis after bringing him in on loan last term.
And the Telegraph claim the club are ready to compete with Chelsea for Song's signature, although he is still likely to move to Stamford Bridge.
Song made 31 appearances for West Ham last season after failing to break into Barca manager Luis Enrique's first XI.
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Chelsea are said to be preparing a £70,000-a-week contract for Alex Song
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The Cameroonian joined Barca from Arsenal for £15m back in 2012 but has made just 25 league starts for the Nou Camp club since.
If he were to move to west London, Song would have to compete with Ramires, Nemanja Matic and former Arsenal team-mate Cesc Fabregas for games in the middle of the park.