Harrison and ex-Maritzburg United mentor Ian Palmer have both been linked with the City hotseat, which was vacated by Duncan Lechesa earlier this week.
Polokwane's fitness trainer Eduardo Schoeler supervised the Premier Soccer League strugglers in a 1-0 loss to Orlando Pirates in midweek.
"He (Harrison) is not going anywhere," Mpengesi tells KickOff.com.
"You must also remember that we still have an outstanding case where we are fighting to return back to the PSL this season.
"We not prepared to lose a coach of his calibre at this moment."
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