It is alleged that the 55-year-old businessman offered a $7500 cheque to bribe the civil servant, court documents viewed by the Herald allege.
The businessman has pleaded not guilty to one charge laid by the SFO under the Secret Commissions Act.
The alleged bribe was over a technology goods contract for the council, court documents read.
The SFO later confirmed the goods were USB flash drives from China.
While working at the council Rasila was tasked with obtaining quotes for the supply of the goods from prospective suppliers, court documents read.
It is alleged Rasila prepared an anonymised price comparison spreadsheet and excluded material price information.
The council then awarded the goods contract, relying on the details of the spreadsheet, the SFO claims.
The supply contract was valued at $152,520 and was varied to $140,150, allegedly as a result of the spreadsheet.
Auckland Council chief executive Stephen Town earlier said in a statement Rasila left the council three years ago after the alleged offending occurred.
He also alluded to the possibility the SFO's investigation came after a tip-off from a whistleblower.
"Despite our disappointment that a former employee of ours is now before the court, we are pleased to see that the tools we have in place to detect wrongdoing, including giving staff the channels and power to speak up, are working and enabled this to be brought to our attention," he said.
Both Rasila and his alleged co-offender will reappear in court on October 16.