The 26-year-old forward spent last season on loan at Plymouth Argyle and scored eight times in 33 League One appearances.
He is not a big part of Birmingham’s plans this season and the club are prepared to loan him out again in the ongoing transfer window.
Charlton are amongst several League One clubs who are interested in getting their hands on him on loan this summer and they are the favourites.
And it has been claimed that the forward will take a decision on his next loan club this week.
Cosgrove is assessing all his options on his table as he decides on which club to join this summer.
Charlton are the leading the hunt to land him and are looking to convince the player to move to the Valley in the coming days.
Dean Holden is an admirer of the forward and is keen to have him as part of his Charlton squad this season.
