Kleiner spokeswoman Christina Lee said: "We remain committed to gender diversity in the workplace and believe that women in technology would be best served by focusing on this issue outside of continued litigation."
Pao, now interim chief executive at social-news service Reddit, claimed her standing at Kleiner Perkins crumbled after she ended a brief affair with a partner, Ajit Nazre. She claimed her career deteriorated after both Nazre and Kleiner Perkins started retaliating against her in a climate that was overall unfriendly toward women, her lawyers argued.
After the verdict, three jurors told Reuters they had focused on Pao's increasingly negative performance reviews, which undermined her argument that she deserved to be promoted.
The venture capital firm is now seeking to recover about $973,000 of its litigation costs, while Pao's lawyers argue she should not have to pay.
Kleiner has said it would waive its legal costs should Pao choose not to appeal, an offer which still stands, Lee said.
A hearing on costs is set for later this month.
Read MoreEllen Pao gender-bias lawsuit is a setback for women
Kleiner's offer to withdraw its costs request in exchange for an end to the case is common when defendants prevail in employment lawsuits. Should Pao decide to pursue an appeal, her case would be heard by California's First District Court of Appeal.
She could face a difficult path. According to Westlaw data, out of 49 decisions involving discrimination and retaliation over the past two years, the First District affirmed 26 of 31 cases where the employer won in the trial court, or 84 percent. Only five cases were reversed.
Meanwhile the court, which covers San Francisco and 11 other Northern California counties, handed victory to employers in more than half of the cases they lost in the lower courts, reversing 10 of 18 cases.