The wealthy businessman reportedly told Russian media that Royals are lining up a January bid for the out-of-favour Gunners midfielder.
Zingarevich suggests 31-year-old Arshavin is just one of several potential transfer targets as manager Brian McDermott looks to bolster his squad in a bid to kick-start Royals' season.
If Zingarevich gets his man, Arshavin would link up with his countryman and ex-Zenit St Petersburg team-mate Pavel Pogrebnyak once again.
Royals' owner told sports website Spb.kp.ru: "Arshavin is interesting for Reading. But he is one of 10 players that we are interested in."
Reading are yet to win in the Premier League following Sunday's 1-1 draw at fellow strugglers QPR and sit two places off the bottom of the table.
They were also knocked out of the Capital One Cup by Arsenal in embarrassing circumstances last week, with Arshavin handed a rare opportunity by Arsene Wenger on the night as Gunners fought back from 4-0 down to win 7-5.
Arshavin has made a total of 142 appearances for Arsenal, scoring 31 goals. But he is suffering from a dip in form and has played just 46 minutes of Premier League football this season.
Wenger could now be open to offers for the versatile forward who cost the club £15 million from Zenit in 2009.
Meanwhile, Royals are facing an anxious wait over the fitness of Alex McCarthy ahead of Saturday's crunch home clash against Norwich City (3pm ko).
The 23-year-old keeper crashed against a goalpost as he dived to cover Djibril Cisse's shot in the dying seconds of Sunday's draw at Loftus Road.
He was due to have a scan yesterday, with Adam Federici poised to step in against the Canaries.
McCarthy put in an eye-catching display against QPR and made two superb saves to deny Esteban Granero and Adel Taarabt and preserve a point for his side.
"The first save [from Granero] was fantastic, pushing the free kick onto the bar, then the one-on-one against Taarabt was another fabulous save," added McDermott. "It was a point-winning save I would suggest.
"He's playing very, very well. He's a cool, mature young man with a really good mindset, he works hard and wants to be the best he can be.
"He's a very good young goalkeeper and we are blessed with good goalkeepers at our club. He's working hard to keep his place and we have Federici, Mikkel Andersen and Stuart Taylor all pushing each other."
McDermott confirmed McCarthy's fitness is now a concern: "He fell on his shoulder and we will have to have a good look at it."