Blues agreed a fee with Spurs for the Republic of Ireland international last week but the move has now apparently stalled over the player's wage demands.
Acting chairman Peter Pannu told the club's official website: "I met with (manager) Alex (McLeish) and (chief scout) Paul (Montgomery) to discuss some new targets - names that we will not be mentioning at this moment in time - as we have decided that the signing of Keane would not be in the best financial interests of the club."
He added: "Everyone knows he is a tremendous player but having considered the overall package (one which certainly wasn't unfair on the part of his representatives to ask for given his talent and experience), Keane's age and the length of contract we felt that financially he wasn't the best option available.
"This is unfortunate because Keane is a class act but supporters can rest assured we are considering other options and will pursue them where financially viable."
Blues have already made one signing from Spurs in the January transfer window, having brought in midfielder David Bentley on loan until the end of the season.
The offer accepted for Keane was understood to be ¦pound;6million. The Irishman, who joined Tottenham for the second time from Liverpool in early 2009, has only started two matches this season for Spurs.
McLeish has continually stressed the need for Birmingham to sign a quality striker.
He is aware a lack of goals has seen them become embroiled in a Barclays Premier League relegation battle this season. Midfielder Craig Gardner is their leading marksman with just five goals.
McLeish is still also hopeful of bringing in Rangers striker Kenny Miller in a deal which could rise from an initial ¦pound;600,000 to ¦pound;1.1million. Miller has also been the subject of an offer from Fiorentina but Birmingham sources indicate the player is edging nearer to being reunited with his former Scotland manager McLeish.