Earlier on Thursday, a US District Judge ruled last week that Levandowski's use of the Fifth Amendment does not prevent Uber from firing him and that the company should not hold anything back in requiring him to reveal more details on the subject of the suspected stolen files.
Levandowski was a key cog in Uber's autonomous vehicle program until demotion last month. "The ruling said Waymo has "shown compelling evidence" that its former star engineer, Anthony Levandowski downloaded more than 14,000 confidential files" before leaving Alphabet's self-driving auto unit.
Levandowski left Waymo in January 2016 and started Otto, a self-driving truck startup that Uber bought for $680 million (524.9 million pounds) in August. Uber General Counsel Salle Yoo made the demand in a May 15 letter to Anthony Levandowski, citing a court order.
Uber has told Levandowski that he must comply with the order to return Waymo documents or face possible termination, Levandowski's lawyers said in a court filing on Thursday.
She went on: "If you do not agree to comply with all of the requirements set forth herein, or if you fail to comply in a material manner, then Uber will take adverse employment action against you, which may include termination of your employment and such termination would be for Cause".
Levandowski's lawyers stated that he was ordered by the company to meet the terms of the order to return Waymo materials or deal with likely dismissal.More news: Will Smith gets embroiled in Netflix debate
The lawyers asked the judge to modify his order so that Uber is not required to fire Levandowski if the engineer asserts his constitutional rights against self-incrimination and refuses to produce documents. "Almost fifty years of Supreme Court precedent forbid the government from putting an individual to such an unconstitutionally coercive choice", they wrote.
The case revolves around Waymo's charges that Uber has acquired an advantage from the information Levandowski took.
Judge William Alsup, who is overseeing the trial, has also previously referred the case to the USA attorney's office for a potential criminal investigation.
The arbitration would benefit Uber above all by keeping the case out of the public's eye and by containing the span of information sharing or discovery. A preliminary injunction to hinder Uber's self-driving technology development during the case has been imposed, but it's unclear to what extent.
For Uber, the bad news is far from over.