Reports earlier this week suggested that the Hammers were preparing an offer to Liverpool for their England winger.
Since moving to Anfield from Aston Villa for a fee in the region of £20million two summers ago, Downing has struggled to hold down a place in the Reds side.
The 28-year-old made 25 starts and four substitute appearances for the Merseysiders in the Premier League in 2012/13, scoring three goals and claiming five assists.
Hammers boss Sam Allardyce is in the market for wide players as he seeks to improve the service to record signing Andy Carroll, now recruited on a permanent basis from Liverpool.
But although Allardyce's right-hand man McDonald is a fan of Downing and would like to see him at Upton Park, he insists the claims about an impending bid are premature.
"He's a very good player," the Hammers coach told talkSPORT. "A player of that calibre and West Ham being involved would be great, but it's all paper talk at the moment."