The Hammers were credited with interest in the 31-year-old yesterday.
And a departure from Old Trafford is likely for Rooney at the end of the season.
However, Everton are said to be confident of pulling off a deal to bring the former Toffees forward back to Goodison Park.
Rooney has previously claimed he would not play for another Premier League club after his time at United ends.
Wayne Rooney is unlikely to join West Ham from Manchester United this summer
Wayne Rooney transfers odds: Where will the Man United legend move?
Tue, March 21, 2017
Click to reveal the latest transfer odds on Wayne Rooney's next club
1 of 7
Click to reveal the latest Wayne Rooney transfer odds according to SkyBet
The chances of us getting Rooney is 100/1 contrary to reports
Get Quotes on Home Insurance
But with Slaven Bilic looking to bolster his attack at the London Stadium this summer, the Red Devils legend has become a possible target.
And Jack Sullivan claims his dad is not overly confident of securing the surprise switch.
He tweeted: "Just spoken to the boss (David Sullivan), the chances of us getting Rooney is 100/1 contrary to reports!
— Jack Sullivan (@jsullivanwhu) March 22, 2017
"I believe it came from his kid wearing an Adrian shirt."
Jose Mourinho won't stand in Rooney's way should he look to leave Manchester United, having explored the prospect of joining the Chinese Super League in February.
But West Ham appears an unlikely end result, with the Hammers also targeting Sunderland's Jermain Defoe and Chelsea's Michy Batshuayi.