The note said that HBO was willing to make the payment "as a show of good faith", but needed time to fund an account for sending payments in bitcoin digital currency or obtain account information from the hackers so it could use a conventional bank wire to transmit the funds.
Variety has opted not to publish the name or email address of the HBO executive from which the message was sent.
HBO declined to comment on the leaked message to Variety, but the publication confirmed the veracity of the email with someone close to the investigation.
However, this week hackers released an email from HBO according to which the network has agreed to pay $250,000 as part of a negotiation over data swiped from HBO's servers.
"It's interesting that they're spinning it as a bug bounty program", said Pablo Garcia, CEO of Aliso Viejo, California-based FFRI North America.
Additionally, the cable network's message to the hacker asked for an extension of the ransom-payment deadline for one week while the $250,000 payment is made and the necessary amount of bitcoins could be gathered.
"You have the advantage of having surprised us", a member of HBO's technology team said in the July 27 email.
"Hackers are not in this game for US$250,000; this probably took them a lot of time and effort", Goel said.
Variety has obtained a copy of another message released Thursday by the anonymous hacker to select journalists in which HBO is apparently responding to the initial video letter that was sent informing the -owned company of the massive data breach.
There were also internal documents, including a report of legal claims against the network and job offer letters to top executives.
HBO has said it was working with forensic experts and law enforcement in response to the attack.