The Romania international is having a medical in Glasgow and could complete his move to the Scottish champions in the next few hours.
McCoist said: "He's in town and we are hopeful that the final bits and pieces can be settled and he can officially become a Rangers player.
"A fee has been agreed and the personal terms are just about agreed as well. It's just one or two other things but we are hopeful it will be done in the next few hours and we can finalise the deal."
McCoist is trying to determine whether clearance is likely to be granted in time for Goian to play in Tuesday night's Champions League game against Malmo.
The Rangers boss added: "I think there is a work permit required but I would hope he would tick all the boxes of getting a work permit."
McCoist also confirmed that Rangers have rejected a bit from Qatar outfit Lekwhiya for Madjid Bougherra.
He said: "I hope Madjid's future lies here but there has been a bid received which we have knocked back from a team in Qatar. That's where we are at the moment.
"I don't want Madjid going anywhere."
McCoist also refused to rule out another bid for St Johnstone midfielder Murray Davidson after Rangers' first offer was rejected last week.