Fortune is available on a free transfer after ending a short stint with Belgian side Tubize and has spelt out his desire to return to England.
Championship side Ipswich - managed by former United captain Roy Keane - are also set to run the rule over the 32-year-old South African in the coming days.
Blues manager Alex McLeish has also invited former Celtic defender Balde to link up with the club when the players report back for pre-season training on July 8.
It is believed City are willing to offer Balde a two-year contract if he creates a favourable impression, although it is understood the 33-year-old has already been offered a permanent deal by fellow promoted club Burnley.
Balde would represent a gamble as he has seen little action at Parkhead in recent seasons after refusing to walk away from a lucrative contract despite being frozen out of the first team.
McLeish is also hoping to complete the £5million transfer of Cardiff defender Roger Johnson.
Johnson has been discussing personal terms with the Premier League side after Cardiff finally agreed to the structuring of the deal on Wednesday.