The Magpies are currently embroiled in a relegation battle, and are just one point outside of the bottom three going into tonight’s clash with Aston Villa.
Bruce has come under fire from supporters this season, and has admitted in recent days that his future at the club ultimately depends on whether or not Ashley decides to persevere with him.
The Toon owner has twice brought in managerial changes in the latter stages of a campaign before, and both times Newcastle have gone on to suffer relegation, with Alan Shearer and Rafa Benitez in the dugout on those occasions.
With that in mind Harmison believes Bruce is not going anywhere.
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Speaking to talkSPORT, the former England cricketer said: “Steve Bruce is here to stay.
"There’s no way Mike Ashley is going to get rid of Bruce now.
"He’s done it twice before with 10 and eight games to go with Benitez and Shearer coming in, and both times he got relegated.
“Ashley will probably stick with Bruce. Newcastle United fans won’t want to hear that, but this is where the reality is of what Ashley’s Newcastle is.
"Newcastle fans have just got to hope they can get something out of tonight, something out of Brighton next week, and then they play Burnley after Tottenham.
"If they can get four of five points out of that with the last two games of the season against Sheffield United at Fulham, they’ll feel as though 38 points will be enough.”