The Frenchman returned to Old Trafford this season buoyed from his World Cup triumph, but has once again proved underwhelming.
With a modest three goals and three assists, Pogba has been a passenger in some games this season, drawing criticism from fans and – more poignantly – his manager.
Pogba was stripped of his vice-captaincy duties after stoking rumours linking him away from Manchester, as well as criticising his team’s tactics after their 1-1 draw to Wolves in September.
The 25-year-old has, as per his time at Old Trafford, shown glimpses of brilliance, but the midfielder is not currently flavour of the month after his abysmal display against Southampton last weekend.
“If I’m Ed Woodward and my champion was Mourinho I’d want to do something quite extreme to support him,” the outspoken Jordan told talkSPORT.
“I’d publicly get right behind him and put a stick right up Pogba’s backside in terms of straightening him out, so he knew where I stood.
“Frankly whoever wanted to sign Pogba in the first place… I’d send them home in a cab!
“I would sell Pogba in a heartbeat.”
Jordan was the Eagles chairman for 10 years before leaving the role in 2010, and has dealt with his fair share of divisive players.
“I think he is a malaise and has far too much to say for himself.
“And most of it has no relevance,” the 51-year-old businessman added.
“His performances on the pitch are far and away beneath what one expects of a player who is reported to be of the quality he is.
“The World Cup success with France was [N’Golo] Kante, [Antoine] Griezmann and [Kylian] Mbappe excelling in their individual roles.
“I think there was a lot of noise and rubbish coming from Pogba inside the dressing room – I think he’s all myth.”