"Marc has made his decision and he will be in Glasgow on Tuesday," he told the Hull Daily Mail. "He will look around the club and do some things which I do not need to be at. We still have some details to discuss with Celtic.
"It is nothing major but with every transfer you have to take care. There are some discussions to be finished but if things are normal he will sign for Celtic.
"I'll arrive on Tuesday night and I expect by Wednesday night everything will be OK for him to sign.
Manuello was hopeful that everything should be completed so that Fortune would be available to fly with the rest of the Celtic squad to Australia on Thursday.
The Hoops arrive in Brisbane at midnight Friday to begin pre-season training with Sunday's Translink Cup match against Brisbane Roar.
"We are aware that the squad is going to their training camp in Australia on Thursday."