Rumours that the French international could head to United for a Premier League record fee of £100 million ($133 million) have reached fever-pitch in the last month, with United's new manager Jose Mourinho on a spending spree in preparation for the new season.
But Allegri said that Pogba leaving Juventus could mean leaving the highest level of football.
Here's what Allegri said:
"I am calm about the English rumours. Anyone who has the opportunity to leave Juventus has to consider things very carefully, because right now Juve are among the top four European clubs.
"This is not a selling club that just lets its players go. Pogba belongs to Juve and at the end of the day he too will want to win another Scudetto and hopefully the Champions League.
"We have grown in terms of appeal and awareness of our own capabilities. So far our market this summer has been eight out of 10, bringing in players of international pedigree like Medhi Benatia, Dani Alves, and Miralem Pjanic."
Real Madrid had also expressed interest in the striker but talks fell through - even though Pogba expressed a preference for the Spanish side over United.
Either way, United does not have long to make the deal if it wants Pogba start in every game - its first Premier League match takes place on August 14 against Bournemouth.
In other United transfer news, Sky Sports reports that AS Monaco right-back Fabinho is now looking very likely to join the team in a £22 million deal. The deal is perhaps partly a result of Fabinho's history with Mourinho - they have the same agent and Fabinho made his only appearance for Real Madrid in 2013 when Mourinho was still the manager there.