The Dutch boss is under huge pressure in the Goodison Park hotseat after a nightmare start to the season.
The Toffees splashed out more than £150million in the summer, but they now find themselves in the relegation zone after a dreadful 5-2 defeat to Arsenal at home on Sunday.
And Campbell, who played over 130 games for the Blues, has urged club chiefs to be ‘ruthless’ and make a change now, rather than later.
Speaking to talkSPORT host Jim White, the former Toffees star said: “I’m of the mind set to give managers time, and I said this a bit earlier on in the season when a lot of fans were saying it’s not happening under Koeman.
“I don’t like anyone losing their job, but it just doesn’t seem to be working. He was skating on thin ice a couple of games ago and obviously now it looks likely they might have to pull the trigger.
“I’m not saying Ronald Koeman is not a good manager, I think he is a good manager, but it just doesn’t seem to be working at Everton.
“It’s not just the results, for me it’s the performances as well. Every team could lose games and when you lose games in the Premier League, it’s fair enough, but when you look at Everton this season, how many times have we been able to say we ran them close?
“They just don’t seem to be gelling. I don’t know what it is, but it’s just not working.
“He doesn’t seem to be getting the reaction out of the players that is required.
“There are a lot of frustrated people on the blue side of Merseyside right now and the owners have got to be ruthless to move the club forward.
“None of us like to see people lose their jobs, but if it’s not working they have to make the decision and move on.”