The former Manchester United man, whose contract expires at the end of the month, has been continually linked with a return to the Premier League, with Cardiff City also thought to be interested in his services prior to their relegation from the English top flight.
Diouf, 26, has enjoyed an impressive three-season spell with Bundesliga outfit Hannover, scoring 35 goals in all competitions.
But the Senegal international - who dislocated his shoulder back in March - rejected a new deal with Hannover, and Coates is confident that Stoke will finally be able to secure his services at the third attempt.
"We're hopeful that Diouf will be done," Coates told BBC Radio Stoke.
"He's the striker (manager) Mark Hughes wanted last year. We thought twice we'd got the deal done only for the deal to collapse, as it does in football."
Coates also revealed that Hughes, unlike predecessor Tony Pulis, is keen get the club's transfer business done early in the window.
"We've got a few irons in the fire with other players," Coates added.
"Tony Pulis had a preference for leaving things late. I wasn't always sure he was right but that's what he felt, so we tended to go down that path.
"Mark would rather do things earlier.
"They're all different. The outcome is the important thing."
