The pair are the two hottest properties in world football at the moment, with Haaland appearing to ignite a rivalry with Mbappe when he admitted the Frenchman's Champions League hat-trick against Barcelona give him a "free boost" for his game against Sevilla a day later, when he scored twice.
And with United are currently second in the Premier League, 12 points off Manchester City, Ferdinand feels his old club need to be in the race for the game's most exciting talents if they want to challenge for the title.
He also demands the club bring in a "commanding" centre-back with pace.
"They finished 30 points behind Liverpool last season, now they're above them.
"That's a big, big achievement in that sense. We were not sitting there last season thinking Manchester United would win the league this season or be up there.
"Four or five weeks ago we were saying that, so I see that as a massive step in the right direction. Is this team in a better position than they were last season? Yes they are. Is there still work to do? Yes there is.
"But I see progress. I still see room for improvement, we definitely need to buy a centre-back, a commanding centre back with pace, please!
"I think [Edinson] Cavani, yes, he's a good stopgap but [we need] a centre forward. If people like Erling Haaland or Kylian Mbappe are available, you can't allow them to go somewhere else and you need to move heaven and earth to get them here.
"'Manchester United are used to having superstars and those boys would change the narrative at this football club, that's how good they are.
"There's room for improvement and opportunity to improve this squad, there's players out there available, it seems. We need to be in the mix."
Mbappe, who has over 100 career goals to his name already, is out of contract in June 2022. It's said that a move to Liverpool would be his preferred next step as opposed to signing for United.
Haaland, meanwhile, was reportedly close to signing for United for just £3 million three years ago but a mix-up allowed Red Bull Salzburg to swoop in and acquire the Norwegian.
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