The 30-year-old Russian believes that with the right investment Royals can become a regular top 10 club in the division.
He spelled out his vision on the eve of the proposed takeover of the club by his Gibralta-based Thames Sports Investment company.
The buyout will see TSI acquire a 51% stake for £25 million, with the option of increasing that share at a later date.
Speaking after Reading FC's promotion parade around the town on Sunday, Zingarevich predicted: "I think we can be a top ten club in England within the next five years.
"It was a fantastic day for the club, the fans and everyone around the town and it was fantastic to be part of it. It shows just how far this club has come and I think we can take it forward now."
Zingarevich's words will be music to the ears of jubilant fans who are basking in the glory of their team's promotion to the Premier League.
Thousands of loyal Royals braved the appalling weather on Sunday to honour Brian McDermott's Championship-winning team.
With flags and banners waving, they lined the streets as an open-top bus parade made its way through the town centre en route to the Madejski Stadium where skipper Jobi McAnuff was officially presented with the Championship trophy.
Afterwards, the players and staff partied well into the night at a private function at the stadium, while the playing squad is due to jet out to Marbella for a four-night celebration later today.
But McDermott is already plotting for next season and Zingarevich has promised to back his manager in the transfer market, with promotion said to be worth around £100 million.
"We want to enjoy the moment but we've started thinking about next season already," said the wealthy Russian businessman. "We'll need to make some signings and that's what we'll be aiming to do. We have a big squad but we definitely need to make some signings."
Zingarevich hoped his TSI takeover would be completed by the end of March but it is still awaiting approval from the Premier League.
However, Zingarevich says the deal could be concluded before the end of the week.
"It's up to the Premier League now," he explained. "They have the documents and they requested some additional ones which we supplied.
"They were at our stadium on Sunday. We really wanted to get it all done before the trophy presentation but it didn't happen. However, I don't think we're far away, maybe before the end of the week.
"I completely understand why it is taking time. They're doing the right things and it's important for the game that everything is examined.
"Reading has been in existence since 1871, there is a lot of history there. I suppose they want to make sure they are letting the right people in.
"Obviously, we want it to go through as soon as possible but everyone around here has already made me feel part of it, even before the takeover is completed. Now I just want the formalities to be completed so we can continue what we've been doing."
Meanwhile, Royals winger Jimmy Kebe faces an eight-week recovery period after undergoing knee surgery last week.