According to The Sun, the ex-Everton and West Bromwich Albion striker is spearheading talks to purchase the newly promoted South London outfit, with current majority owner Robin Stanton-Gleaves involved in discussions.
Bromley are preparing for their first-ever League One campaign after securing two promotions in three years and are seeking significant investment to compete at the higher level.
Anichebe, who scored 27 Premier League goals during spells with Everton, West Brom and Sunderland, is now a businessman and owner of the Lumira Group. He recently backed a £20 million proposal for a major leisure development near Liverpool.
His influence is already reportedly being felt, with Bromley signing Victor Adeboyejo from Luton and taking Bolton defender Richard Taylor on loan. Both players are of Nigerian descent.
Anichebe earned 11 Nigeria caps between 2008 and 2011 and represented the U-23 Eagles at the 2008 Beijing Olympics.