In an interview with CNN Business on Wednesday, Wright said he plans to tell Zuckerberg that he should show up to testify in front of the UK parliament to explain Facebook's approach to data privacy and efforts to stop the misinformation spread.
For Wright, the visit to California with UK Digital Minister Margot James is a way to get input from the companies that will be directly impacted by any future UK regulation – something that is no longer a question of whether it happens, but when and how. 
Wright's visit is the same week as the release of a scathing UK parliamentary report on disinformation and fake news, which likened Facebook to "digital gangsters" that knowingly violated data privacy and competition law.
Throughout the 18-month inquiry, the committee repeatedly asked Zuckerberg to testify. The requests were rebuffed so many times that the committee said it would issue a summons to the billionaire CEO if he ever set foot in the United Kingdom.
In response to the report, Facebook denied it violated any laws and said it's open to regulation.
Regulation is coming
Wright told CNN Business that the executives at the tech companies he's talked to so far seem to recognize the regulation coming in, though they're keen to show him the mechanisms they already have in place . That self-regulation is not enough, Wright said.
"There's an acceptance that the UK government is determined to have a system in place to catch those who do not behave as they should," he said. "Although I do not think anyone welcomes regulation, there's acceptance, this will almost certainly happen, and we're getting a good conversations about how this will take place."
Wright and Home Secretary Sajid Javid will be releasing a white paper in the coming weeks with a range of legislative and non-legislative proposals to address online risks.
Wright said they are considering a range of options, including appointing a new online regulator. But he warned that the white paper is just the starting point.
"This is a consultative process, deliberately so," he said, noting that if the UK enacts these regulations, it will be "groundbreaking." That makes it "so important that you take the trouble to get the details right and talk to those who will be directly affected by it," he added.
"It is important that we do the same while protecting people from harm. .. and at the same time maintain what's best about the internet, "Wright said. "We have to try and strike a balance between them."