Speaking to ABC’s This Week, Jay Sekulo implied any battle could go all the way to the Supreme Court.
It has long been assumed Special Counsel Robert Mueller will want the President to testify in the investigation, but he has not yet officially ben asked.
Mr Sekulo told ABC the Trump team had not broken any specific laws in their election campaigning.
He said: “You have to look at what laws, rules, regulations, statutes are purportedly violated here.
“So when you look at a meeting — when you look at a meeting, George, that took place in — a — a year before the (ph) — now two years ago, the question is what law, statute or rule or regulation’s been violated? Nobody’s pointed to one.
“And we’ve seen 1.4 million documents, we’ve provided 32 witness interviews of any type of collusion on behalf of the president and the Russians.”
He accused Mr Mueller of running “one of the most irregular investigations in U.S. history”.
The lawyer argued the President could use Article II of the US Constitution – the Presidential powers – to refuse any issued subpoena.
A subpoena is a writ issued by a court house or other organised court which orders a person to attend court.
Part of Mr Mueller’s investigation centres around the meeting between Donald Trump’s son, Donald Trump Jr, and Russian lawyers, just months before the election in June 2016.
The meeting took place in Trump tower in New York, and the president originally claimed it concerned the issue of international adoptions.
But on Sunday, Trump tweeted the meeting discussed information and getting dirt on his election opponent, Hillary Clinton.
“This was a meeting to get information on an opponent, totally legal and done all the time in politics – and it went nowhere,” Trump said on Twitter. “I did not know about it!”
Emails released by Trump Jr also suggest the meeting was about getting negative information to use against Clinton in the campaign.
Both President Trump and Russian President Vladimir Putin have said Russia did not interfere in the US election.
But the CIA, FBI, NSA and the Director of National Intelligence have all confirmed with “high confidence” that Moscow worked to influence the 2016 polls, perhaps in favour of Trump.