The 18-year-old has emerged as one of the most sought-after prospects in European football.
It has been suggested that an offer of around €28 million (£24m/$32m) could be enough to tempt Brescia into a sale.
Cellino has offered no indication that is the case, with there a desire on the part of the Serie B side’s president to keep a prized asset in his current surroundings.
Interest is building, though, with the likes of Liverpool preparing more formal approaches after previously watching on from afar.
“I’ve talked about him to [Roma director Mauro] Baldissoni several times, but I want to keep the lad as long as possible.
“Is he ready? I don’t know, he’s 18. But Liverpool also contacted me a little while ago.”
Tonali made his senior debut for Brescia in August 2017 as a 17-year-old.
He scored his first competitive goal towards the end of the 2017-18 campaign and has remained a regular in the side under Eugenio Corini.
He said: “I was an AC Milan fans as a child, as I have always said, but I am not thinking about the future. I am inspired by [Gennaro] Gattuso, by his determination. He always gave everything. I would like to do the same myself. I would like to be coached by him.
“Pirlo comparisons? I feel good playing in any midfield position. I mostly play as the playmaker but I have no problem playing on the sides of the midfield.
“My dream? Going to t Serie A with Brescia.”