It comes amid Manchester United's hot chase for the striker after Erik ten Hag made him his top priority in the transfer window.
The Red Devils are desperate to sign a striker this summer after struggling with Wout Weghorst and Anthony Martial last season.
However, no agreement has been found yet between United and Atalanta and Gasperini has now spoken out on the speculation.
"Hojlund or [Giorgio] Scalvini? I'd rather not lose either of them," said La Dea boss.
"Atalanta can hardly turn down certain offers, and this is the big difference with us and the big clubs.
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"I'm always sorry when one of our best players leaves.
"But you need to sell to reinvest and maybe become even stronger.
"I haven't talked to Hojlund about the transfer market, he's training well, he's a valuable guy and I think he's doing very well here.
"Sometimes it's a question of life choices."
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Atalanta star Scalvini is another player linked with a departure while United might be able to prise Hojlund away with a big enough offer.
However, they are seemingly unwilling to match the £85million asking price.
Nevertheless, having signed Mason Mount and Andre Onana, United will now concentrate their efforts on Hojlund.
Ten Hag's side have already travelled to the United States and their pre-season tour is underway.
And he will want the full make-up of his squad confirmed as soon as possible while some departures are expected as well.
To make up the necessary funds, several players have been mooted for exits while Anthony Elanga is already close.
Nottingham Forest are nearing a £15m deal for the Sweden international, and they are also keen on Dean Henderson in a permanent transfer.
Fred, Donny van de Beek and Harry Maguire could also leave, while Alex Telles and Eric Bailly are closing in on moves to Saudi Arabia.