Yeates is available on a free transfer after being released by Watford earlier this summer.
A number of clubs are thought to be chasing Yeates, but Bradford are hoping to lure the 28-year-old to Valley Parade.
Bradford boss Phil Parkinson is a big admirer of Yeates having worked with the former Tottenham and Middlesbrough man during his time in charge of Colchester.
Parkinson is keen to bolster his attacking options and he sees Yeates as a key addition to his plans as they get ready for life in League One next season.
The other former Boro man in Bradford's sights is Kennedy, who is a free agent after turning down a new deal at Rochdale.
Bradford tried to sign the 26-year-old in January, but Dale turned down their offer - but now City have returned and look set to seal his signature.
Newly promoted Championship side Yeovil also have an interest in Kennedy, but a move closer to his native North East is thought to appeal to the midfielder.