The former Leeds United star, who has failed to establish himself with City is under contract at the Etihad Stadium until June 2020.
The Times has also named Manchester City goalkeeper Joe Hart and striker Kelechi Iheanacho, Arsenal duo Olivier Giroud and Theo Walcott as the Hammers’ targets.
The player himself said earlier this year “It’s been a bit of a roller-coaster ride since I’ve been here, I’ve not managed to get going, but I’m over my injuries now and I feel really good so I’m ready to try to help out my team-mates, a couple of mates have said to me, ‘You’ve been linked with X, Y and Z’ but I’ve not given it any thought. I’m happy here.”