SkySports understands City are thought to have agreed a fee with West Ham for the 23-year-old and are hoping to persuade him to move to Ashton Gate.
A number of other clubs, including Charlton, are believed to be keeping tabs on Baldock's situation, but Bristol City are in pole position to land the former MK Dons hit-man.
Baldock, who joined West Ham last summer, scored five goals in his first nine games for the Hammers, but saw his first-team opportunities dry up in the second half of the season.
West Ham are prepared to offload Baldock with Hammers' boss Allardyce having a wealth of options in attack.
Robins boss Derek McInnes has made Baldock his top target as he looks to bring in a new striker ahead of the new season and is hopeful of tying up a deal for the talented forward.
