Foreclosure Price vs. Bank's New Price: How To Negotiate

[Michael Glaser]

I see a lot of home come up for auction and then purchased back from the bank for pennies on the dollar. 

For example:

Foreclosure Information

JUNE 22 2017	Listed by bank	$31,200	This property was foreclosed and now the lender is selling it for $31,200.Zillow's Foreclosure Estimate predicts this property will sell for $39,618.
FEB 27 2017	Foreclosed	$26,400	The lender assumed this property for $26,400 during foreclosure proceedings and now owns it.

Legal

Foreclosure type: Judicial Recorded: Unknown
I'm wondering if I'd have success making a cash offer with a quick close just above the $26,400 or the 'Foreclosed' price? Most markets are really hot these days and I'd like to find the sweet spot so I'm not spinning my wheels. Or am I safer asking in and around the banking list price?