The Mirror says Jovanovic, 27, is set to leave his club Standard Liege this summer on a Bosman.
The forward was expected to go to Anfield on a free transfer to work under Rafa Benitez after talks in January.
But Jovanovic's future has been thrown into doubt following Benitez's move to Champions League winners Inter Milan.
And now Brum would like Jovanovic to come to St Andrews to link up with his compatriot Nikola Zigic.
Agent Barry McIntosh confirmed: "Birmingham wanted Jovanovic in January and I tried to make it happen but he wanted to run his contract down.
"Now a move to Birmingham is a possibility once more."