Ranieri is not expecting an instant return on Abramovich's investment but he indicated he would be disappointed if Chelsea were not in the running for the title next season.
He said: "It is important to build a good team and it takes time. United and Arsenal spent years doing it and now they are very good. I have a strong team and I am sure at the end of the league we will be very, very, close to the big teams.
Ranieri - whose side lost their first pre-season friendly against Lazio on Friday - acknowledged that Abramovich's millions will increase the expectation levels, but insisted he could cope.
He added: "I want to win things. I am an ambitious coach, I have ambitious players. I like the pressure. In Italy the pressure was crazy. I am used to working under pressure. It is okay and I am ready for it."
Chelsea's opening game is on Friday against Malaysia, who are managed by former Chelsea player Alan Harris. Duff and Bridge are due to fly out to Malaysia this afternoon.