The midfielder's contract at Fir Park has expired and he has been linked with both Hearts and clubs south of the border.
However, McGhee believes his previous relationship with the 26-year-old at Fir Park could be enough to tempt him to Pittodrie.
"I'm fairly hopeful," said the new Dons boss.
"So far Stephen's options that he's been given by his agent and by clubs don't really jump out at him.
"I think we have an advantage in the sense that he knows us and he likes working with us."
Jim Paterson, who quit Motherwell for Plymouth in January 2008, is another target but reports linking Maros Klimpl with a move north are wide of the mark.
"Maros Klimpl is not someone I've been looking at," said McGhee.
On Paterson, however, he added: "He's a good footballer, he's left-sided, he gives you options in left midfield and at left-back.
"I'm just tying to look at all the permutations. Jim Paterson is one that's on the radar."
McGhee is also willing to hold talks with Jamie Smith, who is out of contract this summer and has been linked with a move to Toronto FC.
The former Celtic and ADO Den Haag winger has been plagued by injury during his time at Pittodrie and McGhee has yet to decide whether to offer him a new deal.
He told REDTV: "At this stage, I wouldn't say he is someone I'd like to keep.
"What I would do, I'd like to explore exactly what went on with him, the injuries he has had.
"I've initiated some discussions between the club and his agent and Jamie himself just so that I can try to get to the bottom of why someone who could really be a good player for Aberdeen is leaving and why he has had these injury problems.
"I just want to examine that. I'm not saying at the moment we are going to re-sign but I'm going to look into it."