The two clubs are in talks to discuss a potential swap deal that would see Kyle Walker-Peters to move to the London Stadium with Downes joining Southampton.
Downes spent last season on loan at Southampton and the club have been keen to sign him for the long-term following his role in getting them promoted.
Saints would still have to pay a fee for Downes even if Walker-Peters moved to West Ham, but the two deals could be structured separately as well.
It has been claimed that the Saints have now thrashed out an agreement over a long-term contract with the West Ham midfielder.
Downes has been keen to return to Southampton following his impressive loan spell under Russell Martin.
West Ham would still have to agree personal terms with Walker-Peters and thrash out an agreement with Southampton.
And it is suggested there is a valuation gap between the two sides regarding Downes.
Downes is keen on the move and is now waiting for the other pieces of the jigsaw to fall in place for the deal to go through.
