Inter are holding their valuation at €70m and have already rejected an opening bid of €45m from the Catalan club.
Chivu was blunt in his latest public comments on the situation.
"Bastoni is one of our champions. It is normal that there are transfer rumours around him because, for me, he is one of the best centre-backs in the world. I know what kind of person Alessandro is, but above all I know what he has given us, what he gives us and what he will give us in the future."
In an earlier statement that month he had been careful not to overreach but equally clear about his position.
"I must give him serenity and trust, to him as to the others. I can't control his future, what he wants to do. I know he is very happy at Inter and to be part of this wonderful group."
Bastoni, 27, made 296 appearances for Inter having joined the club from Atalanta in 2017 and is contracted until June 2028. He played through an ankle problem in the final weeks of the season and was a cornerstone of the double-winning campaign — Inter Milan claimed both the Serie A title and the Coppa Italia under Chivu.
His summer has been complicated by the controversy surrounding Italy's failure to qualify for the World Cup, for which he received some blame after being sent off in the play-off final against Bosnia and Herzegovina — a match Italy lost on penalties.
Barcelona's pursuit has cooled in recent weeks. Head coach Hansi Flick is understood to have developed reservations about Bastoni's profile, preferring a centre-back with different technical characteristics. That has opened the door for Real Madrid, whose interest in the Italian was confirmed by Gazzetta dello Sport, with incoming head coach José Mourinho described as an admirer.
Inter sporting director Piero Ausilio has been consistent throughout.
"We want to keep Bastoni. We are happy to have him. Inter certainly won't be the ones calling anyone to offer him for a transfer. He's a huge asset for Inter and for Italy."