The deal has been delayed while Premier League officials investigate Thames Sports Investment, the venture set up by Zingarevich and partner Chris Samuelson as a means of buying the club.
TSI are set to acquire an initial 51% stake for £25 million, with the option of buying more shares at a later date.
That looks to be shrewd business by Zingarevich, with Reading's promotion to the Premier League believed to be worth an estimated £100 million alone.
However, Madejski has promised to stick to the original price agreed with the 30-year-old Russian back in January.
TSI's takeover has been investigated by Football League and then Premier League chiefs ever since, but Madejski believes it will be rubber stamped within days.
"The whole thing is still going through the necessary checks but we think it could be completed next week," Madejski told BBC Radio Berkshire.
"Promotion is just as important to Reading as city status, the economic benefits are huge."
Reading has been gripped with Premier League fever ever since Mikele Leigertwood's late goal against Nottingham Forest sent them up on Tuesday night.
While the playing squad celebrated in London, Madejski, manager Brian McDermott and a sprinkling of backroom staff celebrated long into the night at Reading town centre bar The Purple Turtle, owned by hardcore Royals fan Danny Fraifeld.
The impromptu visit was filmed by fans and is now a massive hit on youtube.
"We got back to the Madejski Stadium at six o'clock in the morning which tells its own story," added Madejski.
"When I got involved with Reading 22 years ago I saw it as a sleeping giant. Now the giant is roaring again."
TSI have already announced their intention to expend the MadejskI Stadium from 24,000 to 38,000 capacity if the team survives its first year in the Premier League.
They also plan to pump fresh investment into the Royals Academy and upgrade the club's Hogwood Park training ground.
And Zingarevich has already confirmed club scouts have been searching for new players, with Sunderland's Kieran Richardson and Blackpool's Matt Phillips linked with moves to Berkshire.
Reading will be looking to clinch the Championship title this Saturday when they host Crystal Palace at Madejski Stadium (3pm ko).