Greene told an event organised by Fortune Magazine in San Francisco on Wednesday that she "wouldn’t have minded buying them, but it’s OK", the news agency Bloomberg reported.
Earlier this month, CNBC reported that Google was talking to GitHub for several weeks but did not offer anything close to the US$7.5 billion ($9.79 billion) that Microsoft offered for the source code repository.
The founder of GitHub, Chris Wanstrath, is said to have chosen Microsoft because of his relationship with chief executive Satya Nadella.
Microsoft has faced some disquiet after the sale was announced, with many developers leaving.
And last week, 97 open-source developers threatened to move their projects away from GitHub unless Microsoft ended its contract with the US Immigration and Customs Enforcement.
Google is also looking at other acquisitions and Greene is believed to have indicated that the company has an interest in open source vendor Red Hat which has obtained a number of certifications from the Department of Defence.
Part of the reason why Google is looking at Red Hat is to bolster its security credentials as it looks to bid for a huge Defence deal worth about US$10 billion known as the Joint Enterprise Defence Infrastructure, or JEDI, program.
Red Hat also supplies its products to the NSA, with the spook agency running its XKEYSCORE program — an application that The Intercept, the website run by journalist Glenn Greenwald, describes as NSA's Google for private communications — for the most part on Red Hat Linux servers.