Two days of intense talks took place with Villa holding out for £18m cash, says The Sun.
"A final deadline to conclude this episode was set that all parties agreed to. This deadline has passed so Gareth will remain with Villa."
The speed in which Villa closed the debate stunned Liverpool and Barry, 27, but the Kop remain determined to get the midfielder.
They had agreed to pay £18m but there was haggling over the methods of payment and Liverpool asked for a small deadline extension.
Villa chief Randy Lerner refused and, even though Liverpool had everything in place by 5.15pm, Villa would not negotiate further.