Press Association Sport understands the Black Cats are looking to take advantage of new Hammers boss Slaven Bilic's squad re-shaping programme to persuade the 30-year-old England midfielder to return to his native north-east.
Downing made 43 appearances for the London club last season, but has been linked with a move away from Upton Park this summer.
He began his career at home-town club Middlesbrough and had a loan spell at the Stadium of Light in 2003 before making a £12million switch to Aston Villa in July 2009 in the wake of Boro's relegation from the Barclays Premier League.
Downing was on the move again two summers later as Liverpool invested £20million in his services, although ultimately he did not fit into manager Brendan Rodgers' plans and was sold to West Ham during the summer of 2013.
He has rebuilt his reputation under Sam Allardyce at the Boleyn Stadium, but the Black Cats are hoping they can tempt him back home as they attempt to bolster a squad which has had to produce late pushes in each of the last two seasons to avoid relegation.
Advocaat and sporting director Lee Congerton have been working hard behind the scenes to land the men they want, and they have shown no lack of ambition.
Despite reports to the contrary, the Dutchman is understood to have tested the water with PSV Eindhoven over their Holland midfielder Georgino Wijnaldum, but the package on offer was not acceptable to them.
Source : PA
Source: PA