The Canaries have slipped back into the danger zone and are now just two points above 18th place following Wednesday night's 2-0 defeat at West Ham.
In an interview with BBC Radio Norfolk and Archant, McNally said: "We are too close for comfort.
"Chris has been told in no uncertain terms 'get us out of that position and keep us out', but equally, we're three points off 10th."
McNally continued: "As far as giving any certainty for Chris, or anyone else - it's a results business. Whether that's Chris Hughton as manager or me as chief executive or anybody else, we're paid to do our jobs.
"As long as we achieve what is required of us, then we'll stay in work.
"It would be wrong at any level, delinquent almost, to give any guarantees.
"All I would assure Norwich supporters is that we are watching it very carefully.
"The whole board is aware of the strength of feeling from the support."
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