Di Marzio claims the Premier League threw out the bid on Monday night.
Referencing reports that Pogba's agent, Mino Raiola, is looking at the Nou Camp as a possible new home for his player, Ferdinand said: "Don't you dare allow this ED..."
It adds that another of Raiola's clients, Paris Saint-Germain midfielder Marco Verratti is wanted by United.
United could do a lot worse than attempting to bring the 27-year-old to Old Trafford although there would be competition for his signature.
World Cup victor Paul Pogba is also unlikely to be fit for the game at Old Trafford.
Willian has suggested he would be happy to stay at Chelsea for the 2018-2019 but the 29-year-old has left the door ajar for a reunion with Mourinho.
Striker Romelu Lukaku showed his all-round quality in Belgium's run to third place at the finals and proved he can offer more than being just a battering ram target.
Mourinho has signed Brazil midfielder Fred this summer, though, which should help free up Pogba's role as a more attacking threat.
The two frequently clashed last season, arguing over Pogba's best position, while Mourinho put their relationship under further strain with some questionable comments about his midfielder's performances at the World Cup.
The Chilean scored just three times in 18 games as United ended the season without a trophy.
The 25-year-old returned to training this week after extra time off following France's World Cup win last month.
Italian daily Gazzetta dello Sport claims the Croatian will meet with club president Florentino Perez to express his desire to leave the club. Mourinho appeared to question Pogba's effort and heart while playing for his club, saying, "I don't think it's about us getting the best out of him [at Manchester United], it's about him giving the best he has to give".