The 27-year-old striker is set for the Foxes after Peterborough United accepted a reported offer of £3million.
Premier League new boys Norwich were interested in Mackail-Smith earlier in the year and Posh director of football Barry Fry claims they made an approach for the forward.
However, McNally flatly denies this claim and he posted on his Twitter account on Tuesday that City had not returned for the striker since they dropped their interest last season.
He wrote: "For the record, CMS (Mackail-Smith) did not turn down Norwich City, despite what Barry Fry might say. Our interest ended in March."
Meanwhile, West Ham are understood to be considering an 11th hour bid while QPR are also interested in Mackail-Smith.
"We have accepted a bid from Leicester," said Fry on Monday. "Their manager Sven-Goran Eriksson is out of the country at the moment, but was due to speak to Craig over the weekend.
"I have had several conversations with West Ham, but we have turned down their bid. I am certain they will be back.
"Craig is facing a tough decision. He turned down Norwich and he has now turned down QPR.
"Craig met QPR manager Neil Warnock and was impressed with him, but he wanted assurances that Neil would still be manager at the start of the season and didn't get them."