Keown, a member of the Arsenal Invincibles team of 2004, didn't just have the fan to contend with, as arch-enemy Simon Jordan also challenged him about Arsenal's faltering campaign.
The Gunners have slipped further out of title contention following Saturday's 2-2 draw against Aston Villa which sees them sitting six points adrift of leaders Liverpool having played a game more.
One win in the last five games means the season has quickly turned on its head for Mikel Arteta's men.
An FA Cup exit at the hands of Manchester United and the deck stacked against them in the Carabao Cup semi-final second leg against Newcastle, trailing 2-0, means Arteta's side could again finish the season without a trophy.
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Things are far from rosy across north London where Spurs are slumped in 15th place having collected just one point from a possible 18.
However, unlike Arsenal, Ange Postecoglou's side do hold realistic hopes of landing silverware in the League Cup and Europa League and are still competing in the FA Cup after seeing off non-league Tamworth earlier this month.
One Tottenham fan called into the White and Jordan show to point out that not only do Spurs have a greater chance of winning silverware than Arsenal, but the current plight of Tottenham is not too dissimilar from their north London rivals.
But Keown was having none of it.
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The former defender kicked off his monologue with a dig at both Tottenham and the caller, saying: "One thing I will congratulate Postecoglou on is that he tried to change the culture. When you guys were celebrating when you failed to get a result against Man City [last season] and it looked like they were going to be champions and denied Arsenal doing it.
"You've got to set your own goals," he continued. "That's what this manager's been doing, but you're an old fashioned fan who's just concerned about what you do against Arsenal. As long as you beat Arsenal every year, that's all you're worried about.
"How can you compare Arsenal and Tottenham right now? They're polar opposites."
Pressed on the differences between the two teams, Keown added: "Look at Arsenal's defence, it's conceded the least amount of goals this season.
"Spurs are up there now they're losing game after game - 12 defeats. That's hardly comparable with Arsenal is it?"
Jordan interjected to highlight the point the caller was making, before aiming his own dig at Keown.
"Well, he does have a point, Martin, because you do write newspaper articles saying you wouldn't have any Tottenham Hotspur players in the Arsenal team," said the former Crystal Palace owner.
"But he does have a point, he says they can win the Europa League and the League Cup.
"You can't win the League Cup, potentially, because you've got to overcome Newcastle at St James' Park after losing 2-0."
Keown hit back reminding Jordan that the tie is far from over, saying: "Well Bournemouth went there at the weekend and won 4-1. If Bournemouth can do it, maybe Newcastle are sitting nervously."
"We will see," Jordan responded. "You would have expected Arsenal to have done their job at home.
"So what he's [caller] doing is drawing a parallel which is what you like to do and sitting in a position of, as we all know and everyone in the studio knows, you have no objectivity as far as Arsenal are concerned."
Tapping into his inner Arsenal, Keown launched a staunch defence of his support for the Gunners.
"Would you expect me to?," he replied. "I played 449 games for them. I won three Premier Leagues, three FA Cups. I have to have a team in this.
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"I would have thought Palace is your team?," he told Jordan. "If you really love Palace, your affinity would be with Palace but I don't really sense that."
"But I'm not stupidly biased," Jordan said in response.
"I'm not being stupidly biased," said Keown. "I think you'll find that's not the case. I was very magnanimous last week when Manchester United knocked Arsenal out of the FA Cup."
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But Jordan had the final say on the debate again clarifying the caller's initial claim.
He said: "The point the caller is making is that Tottenham can win the League Cup, you can't, potentially. Tottenham can win the FA Cup, you can't. Tottenham can win the Europa League and it's very unlikely you're going to win the Champions League."