HITC Sport understands that Tony Mowbray is looking to work with the striker for a third time in his managerial career.
The 34-year-old striker is currently without an employer, and therefore able to join a new club outside of the transfer window as a free agent.
A two-year spell with Wigan Athletic was brought to a close at the end of last season, with the Latics releasing him following their relegation out of the Championship.
It could be that he ends up in League One after all, though, with Coventry ready to put terms to him.
Fortune will join the Sky Blues with a wealth of experience behind him, but a CV in English football which has hardly been prolific in front of goal for both West Bromwich Albion and Wigan.
He was, however, able to break into double figures during a season with Celtic in 2009/10, with Coventry boss Tony Mowbray taking him to Parkhead having previously spent time working with him at the Hawthorns.
A reunion could now be on the cards, with Mowbray confirming at his press conference earlier today – as covered by the Coventry Telegraph – that the arrival of another forward is imminent.