The former Manchester United midfielder was named Serie A Player of the Season last term as he helped Napoli to their Scudetto triumph.
Giammarioli admits management accept McTominay is capable of joining a bigger club and says it's only a matter of time before he leaves for greater things.
Speaking on talkSPORT, he said: “Of course we’re worried.
“But Scott deserves to keep progressing. Maybe not now, maybe not next season, but if the right opportunity comes along in the future, he’s earned it.”
He added: “It’s difficult for Italian teams — the league is still losing revenue.
“We’re trying to grow and remain competitive, but keeping top players isn’t easy.
“It wasn’t simple to bring players like McTominay in — keeping them is even harder. Every decision we make in the market has to be smart.”