(CNN) President Donald Trump's lawyer Rudy Giuliani said Wednesday that special counsel Robert Mueller could still try to seek additional answers from Trump on questions of potential obstruction of justice, but he signaled they will fight any questions they believe violate executive privilege.

"It's not on the table, but could be put back on the table," Giuliani told CNN of obstruction questions.

Trump submitted written responses to the special counsel's office on Tuesday to respond to questions surrounding collusion between Russian officials and Trump's team during the campaign. But Giuliani made clear the process isn't over and the President's legal team is willing to answer follow up questions from Mueller's team.

"We'll consider them and answer them if necessary, relevant and legal," Giuliani said. "If it was something that would be helpful, relevant — not a law school exam."

The written responses submitted to the special counsel on Tuesday came following months of negotiations between Trump's legal team and the special counsel over how exactly the President would answer questions in the Mueller investigation.

The responses dealt with events during the presidential campaign and before Trump was sworn into office, but there are still looming questions about how much Trump's legal team addressed events during the presidential transition in its responses, as well as any additional questions from Mueller. The prospect of an in-person interview with Trump is also unresolved, although Trump said this week that was "probably" off the table.

The thinking of those in the President's circle is that the new acting Attorney General Matt Whitaker would not approve of a subpoena for a presidential interview if Mueller's team goes that route, according to a source close to the President.

Trump's legal team has signaled they'd fight questions about the transition and Trump's time in the White House on the grounds of executive privilege. Giuliani said they would likely argue that Mueller's team got what they needed on obstruction of justice questions from other witnesses, and if Mueller's team delves deeper into the issue it "would involve a real intrusion into privilege."

But Giuliani also noted there was a "gray area legally" when it came to the presidential transition and executive privilege, since Trump had not yet taken office.

Giuliani described the questions as a law school exam: complex with subset questions. He said the questions included what Trump knew about Donald Trump Jr.'s June 2016 meeting with the Russians at Trump Tower, as well as asking about the President's own comments about dirt on Hillary Clinton following the meeting at Trump Tower and his comments asking Russia to find Clinton's missing emails.

Giuliani said that the special counsel's office had indicated they will respond quickly to Trump's answers — he said it could be a week to 10 days — and said they would "in good faith determine do we really need any more."

One of the delays in returning the response was speculation among Trump's legal team that Mueller would release indictments before Thanksgiving, according to a person who speaks to the President. And they were worried about sending the responses without knowing what Mueller might do in the short term. But in the end, they decided to just send the answers in, the person said.

"I don't think there's an answer that will surprise them very much," Giuliani said of the responses. "None of the answers have changed. Maybe we corrected a date or two. Nothing important changed."