The Royals are looking to strengthen their squad during the transfer window after suffering relegation from the Premier League and Zingarevich has been working hard to close a number of deals quickly.
He is hoping to make two signings in the next couple of days and says there will be several more transfers for the fans to look forward to before the end of August.
"I think there will be five to seven new players coming in, including a couple this week," he said in The Sun.
"We have the targets locked up and, hopefully, they will work out."
Reading have already brought in experienced full-back Wayne Bridge after his Manchester City contract expired.
Reports suggest they are also on the verge of signing former Everton and Real Madrid winger Royston Drenthe, who is expected to leave Russian club Alania Vladikavkaz following their relegation from the top flight.