The pair were involved in a heated back-and-forth on Monday following the Red's Carabao Cup final defeat.
Arne Slot's side were beaten 2-1 by Newcastle at Wembley Stadium on Sunday.
The loss followed their Champions League exit to Paris Saint-Germain last week.
It means that Slot can now only win the Premier League in his debut season at Anfield.
With nine matches remaining, Liverpool sit 12 points clear of Arsenal at the top of the table.
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However, Keown believes the Gunners would be more harshly treated if they had the same week as their title rivals.
Appearing on White & Jordan, the former defender said: "If this was Arsenal losing two major games like that, you'd say they bottled it.
"They [Liverpool] have just gone out of the Champions League and they've just lost 2-1. You'd be saying Arsenal have bottled it."
Jordan hit back, though, replying: "No, I wouldn't because they're going to win (the league)."
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Keown quickly pointed to the talkSPORT co-host's criticism of Newcastle's cup final celebrations.
He added: "You would because that would be the mischievous part to your personality. We're seeing all of it exposed here this morning.
"You've no love for the fact that a team has won a trophy after 70 years and you can't find in your heart to see any joy in that. But you want to aim at an easy target.
"But I'm going to say, no, Liverpool, that was taken away from them by a very good Newcastle and Liverpool haven't bottled it at all."
Jordan then responded: "So let's get it right, you've just asked the question, answered it yourself, created an added debate with yourself.
"I would not suggest, if Arsenal won bugger all, which is what they do do right now, I would say they bottled it. If Liverpool lose the league now, what do you think I'll say?"
Keown replied by admitting: "Liverpool aren't going to lose the league. I'm talking about what just happened. What have they just lost?"
The former Crystal Palace chairman continued by arguing: "So you can't make the argument they've bottled it, can you?
"And you can't compare it to the argument that I made with Arsenal who were eight points clear in the one competition that they could win, and they didn't.
"Liverpool had three opportunities to win a competition. If they win one of them, I'm not going to turn around and say they've bottled it.
"And by the way, I wasn't in the camp of saying they were going to do a treble either."
Keown went on to ask: "What is the difference between what Liverpool have done this week?"
Jordan quickly butted in, though, exclaiming: "Because they're going to win something unlike your lot you bloody clown. You need to put a bow tie on and a squirty flower. It makes no sense."
The former England international was able to finish his point, stating: "They get so close to winning something and they don't, and they're bottle merchants.
"I don't think that, I don't like that word. I don't like it aimed at anyone. I just think they've had a very difficult week.
"PSG were absolutely remarkable in the way that they played. And Newcastle were exactly the same."
Liverpool are now out of both domestic cups as well as the Champions League, having previously been beaten by Plymouth in the FA Cup.
As for Arsenal, who have not won a major trophy since 2020, they could still end their wait for European glory.
Mikel Arteta's side face Real Madrid in the Champions League quarter-finals next month after dumping out PSV Eindhoven.
However, the Gunners are set for a third consecutive second place finish in the Premier League.
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