The former Rangers boss is a big admirer of the Celtic midfielder, and was reported earlier this week to test the Hoops's resolve by tabling an offer around £6million.
But McLeish has now switched his attention to adding firepower to his side, and believes he has more than a 50-50- chance of securing Robbie Keane on loan from LA Galaxy.
McLeish has set a deadline of Monday to conclude a deal with the Ireland captain. But he has already closed the door on a move for Ki and said: "Am I interested in Ki Sung-Yueng? I think that one would be not happening because we can't add to the wage bill."
McLeish would not have received any encouragement from Celtic had they proceeded with their interest in the South Korean.
Neil Lennon is reluctant to allow any of his first-team squad to move during this window, and he considers Ki to be an important member of the team.
Midfield is the strongest area of the squad, and this has been noted by other clubs who believe there might be players available to snap up.
Kris Commons has struggled to make any impact this season after his spectacular start at the club, and Southampton are the latest club reported to be ready to offer him the chance to return to England.
But Lennon is only interested in getting Commons fit and back in his side – and he should be back in contention for a place next weekend.
One man who would be allowed to leave is Morten Rasmussen, who is back at the club after a loan spell in Turkey.