The reigning champions go into the new campaign as favourites after winning the league and Italian Cup last season, but Chivu knows his team will face a different challenge this time around.
"We're the team to beat," the Inter manager said ahead of the opening game at San Siro.
That status brings greater expectations, with every opponent likely to see Inter as the side to overcome.
Chivu wants his players to embrace that pressure and show more aggression when the key moments arrive.
"I want us to be bolder, more assertive at certain moments," he said.
Inter have also made significant changes to their squad during the transfer window.
Goalkeeper Josep Martinez is expected to replace the experienced Yann Sommer, while Francesco Acerbi, Matteo Darmian and Stefan de Vrij have all departed.
John Stones has arrived from Manchester City, while Djed Spence has also joined as Inter look to add youth and Premier League experience to their defence. Manuel Akanji has also made his move permanent after spending last season on loan at the club.
Denzel Dumfries, meanwhile, has left for Real Madrid.
There have been changes further forward too, although captain Lautaro Martinez and Marcus Thuram remain the main attacking threats. Young forwards Pio Esposito and Ange-Yoan Bonny are expected to provide additional options.
Inter are also continuing to strengthen their midfield and have been linked with Liverpool's Curtis Jones.
The club will be looking to improve on their disappointing European campaign last season, when their Champions League run ended in the knockout play-off round against Norwegian side Bodo-Glimt.
Midfielder Hakan Calhanoglu remains confident that Inter can continue collecting trophies.
"The objective is always to win, always to dominate the league," he said. "In five seasons I've won eight trophies and played in two Champions League finals, and we'll keep trying to win titles."
Chivu has warned, however, that his squad will need time to reach full fitness after a disrupted summer, with several players returning late following the 2026 FIFA World Cup.
The manager believes the team is still "missing a few pieces" in terms of sharpness but expects that to improve over the opening weeks.
After pre-season tests against Manchester City, AC Milan and Juventus, Chivu will now begin putting his tactical plans into practice when Inter face Monza.
AC Milan manager Ruben Amorim has deployed attacker Samuel Chukwueze in a new wing-back position at the start of his tenure with the Serie A giants ahead of the 2026/27 league opener.
Curtis Jones has left Liverpool after 16 years at the club, joining Inter Milan on a long-term deal that keeps him at the Italian champions until 2031.
Inter Milan have agreed a deal to sign Liverpool midfielder Curtis Jones after all parties accepted the proposed move ahead of the start of their 2026/27 campaigns.
Aston Villa have strengthened their squad ahead of their return to the Champions League by completing the signings of Japan goalkeeper Zion Suzuki and Italian defender Matteo Ruggeri.
