Speculation over the future over the Trotters defender lingered during the winter transfer window with a number of sides linked with Shittu, including McLeish's promotion hopefuls.
Blues managing director Karen Brady wrote in her column in The Sun last Saturday that Wanderers chairman Phil Gartside offered the former Watford man on loan with first option on signing the centre-back.
But the Birmingham boss has denied the proposed deal, contrary to Brady's comments, insisting he is happy with signing Portsmouth's Djimi Traore on loan instead.
UnavailableMcLeish told the Birmingham Mail: "He (Shittu) wasn't offered to us on loan.
"(Bolton boss) Gary Megson said he wasn't available. I think the MD was tongue-in-cheek. Certainly Gary ruled it out. I spoke to him personally. But I know the board said if he was available, they would do it."
Left-back Traore joined on loan from Pompey with Blues paying a small portion of his wages.
As for whether it seemed increasingly unlikely a centre-half would be drafted in, McLeish said: "There's nothing there just now. We've kind of exhausted things. We've had offers of players who are out of contract and haven't been playing for a long time.
"But I think it's too risky especially if it's people we don't know, which is why we took the chance to look at Ulises de la Cruz and Stephen Carr. We know these guys.
"But bringing in somebody in from [say] Argentina, who hasn't played for six months, regardless of who it is, you have your doubts."
Free agent right-back Carr could be offered a short-term deal to help tide Blues over.
McLeish added: "We are still looking at Stephen and assessing him."