There appears to be uncertainty over Moyes' future at the club despite guiding them to Conference League glory, the club's first trophy since 1980, less than two months ago.
Jennings, known for his outspoken views, says West Ham's poor form in the Premier League means the club should pursue a different route regardless of their success on the continent.
It's safe to say Ferdinand doesn't agree as he took Jennings to task over his recent claims about the Scot at the TNT Sports launch in London.
Rio: I said to the lads I was coming on here and one of them said to me that you were talking about how David Moyes should still be given the sack. Are you sure?
Rory: I'm sure.
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Rio: Come on, man! They won a European competition, man.
Rory: Does that not paper over the cracks? They got 40 points in the Premier League [last season], they lost 20 games in the Premier League.
Rio: But they might say 'We were actually focusing elsewhere because we had a real belief that we could win a European competition.' How many managers have won European competitions?
Rory: It's a very impressive achievement but I think there's a ceiling with Moyes and I think that they're really going to pay for backing him this year. Do you not think there's a world in which he could've won that trophy and then bowed out on a high? Because ultimately in terms of being the manager for a Premier League campaign he's going to struggle.
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Rio: The only way where that happens where he wins a European competition and bows out is if he says 'It's time.' I don't think the club could in any way shape or form say, 'Listen thank you for that but you've got to go, you're not good enough.'
Rory: Six weeks before West Ham won that trophy in Prague they played away at Craven Cottage and there's a 'Moyes Out' banner in the away end.
Rio: Yeah but he was an idiot, whoever put that up. It doesn't make it right, does it?
Rory: No, it doesn't make it right but it means that the concerns the West Ham fans were having haven't totally evaporated because they won European silverware, does it?
Rio: I don't think West Ham were great in the league... but listen man, you can't go away from the fact that they've gone into a European competition and won it.
Unai Emery is looked at like an absolute genius because he's won European competitions. Maybe not the Europa Conference League I understand, but he's won European competitions outside the Champions League. There's something to be said about being able to do that, it's not an easy thing to do. It says that he actually is a good manager, he's proved over the years he's a good manager.
Host Hugh Woozencroft then interjected and made the point about how West Ham are yet to spend any of the money gained from Declan Rice's British-record transfer to Arsenal.
And Ferdinand, who begun his career at West Ham, suggested the club needs to do more to allow Moyes to rebuild the team after Rice's departure.
Hugh: The lack of transfers this summer though...
Rio: Yeah, that's a killer.
Hugh: If everything you say about David Moyes is right, the club aren't sending the message of faith and belief about him.
Rio: Is that down to David Moyes?
Hugh: We're talking about quibbling over an extra £3million for James Ward-Prowse.
Rio: But is that him or is that the recruitment and is that the owners? You need that clarity. Is that Moyes saying, 'We shouldn't pay over the odds and £3million is way too much and I don't want to do that, or I'm not sure if he's the right man and I'm not sure I can make a decision.'
Hugh: But if it's the owners, they're not backing him. When we were speaking to West Ham fans last night, they were saying back him or sack him, it's one or the other.
Rio: You can't sack David Moyes, man.
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Hugh: Then back him right?
Rio: I believe they have to back him. Listen you've got £105million that you've just got for Declan Rice. Go and spend it, man. Go and gamble that and put it on people.