The forward is wanted by West Ham and Wolves but they may now be pipped by their relegation rivals.
City have reached agreement with Spurs to pay an initial £4m for the Republic of Ireland international. But this could rise by additional £2m via various add-ons and clauses in the deal.
On his way: Robbie Keane (right) may have played his last game for Tottenham
Birmingham have been given permission to hold talks with Keane but the former Liverpool player has yet to discuss personal terms with the midlands club.
City manager Alex McLeish is a known admirer of Keane, who has been told he can leave White Hart Lane after slipping down the pecking order.
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.
Old pal: David Bentley could soon be joined by his Tottenham team-mate Keane
If Keane does move to St Andrew's he will join up with winger David Bentley, who has moved from Spurs on loan for the remainder of the campaign.
Keane spent the second half of last season on loan at Celtic and has had only a bit part role at Spurs this season.
McLeish is still also hopeful of bringing in Rangers striker Kenny Miller in a deal which could rise from an initial £600,000 to £1.1m.
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.
Explore more:People: Robbie Keane Places: Birmingham, Republic of Ireland
Source: Daily Mail
Source: Daily Mail