Meanwhile, Chiesa is also predicting that goalkeeper Alisson Becker will remain at Anfield despite reported interest from Juventus.
Chiesa spoke to Gazzetta dello Sport, with Liverpool undergoing a significant transition following the departures of Mohamed Salah, Ibrahima Konaté and Andy Robertson and the appointment of Andoni Iraola as manager.
On Jones, the Italian winger was direct.
"All he asked me was what life is like in Italy. I told him it's great and the weather is better than in Liverpool which, other than that, is a special place. Jones, technically, is a really good player. Inter do well to think about signing him."
Jones, 24, came through Liverpool's academy and has been a regular contributor over the past two seasons, though his long-term role under Iraola is not guaranteed given the squad changes under way. Inter Milan sporting director Piero Ausilio has been linked with the midfielder and is known to be interested in Premier League-based talent.
On Alisson's future, Chiesa was equally confident.
"From what I hear, he's staying in England. Then let's see. We're talking about one of the top five goalkeepers on the planet. He's a fantastic leader. He's won everything and makes the difference on the pitch and in the dressing room."
Juventus had identified Alisson as their first-choice goalkeeper target, but Liverpool blocked any approach emphatically.
Chiesa himself is planning talks with Iraola about his own Liverpool future following a debut season at the club that ended with injury.