The Mirror says Blues boss Alex McLeish was in the crowd to see Serbia beat South Korea 1-0 at Craven Cottage last Wednesday.
But the deal has been shelved due to a cash wrangle with agent Barry McIntosh who was commissioned to do the transfer.
McIntosh, who previously introduced former fans' favourite Mauro Zarate to City, also scouted Christian Benitez for City.
But McIntosh has since reported Birmingham to FIFA after clashing with the club's previous regime over the summer transfer of Benitez.
McIntosh said: "I was about to get Jovanovic for Alex McLeish but the situation has become precarious as I've a legal case pending with FIFA over the transfer of Benitez."
Everton have a long-term interest in Jovanovic and it is understood the Goodison club bid over £10m for him last season.