Mr Kawczynski said he would be meeting top London barristers on Friday to talk about the possibility of challenging the law introduced last month by Labour MP Hilary Benn.
Ironically, he said, the Benn Act may actually fall foul of European law.
Mr Kawczynski said he had informed the Chief Whip and invited Conservative Party whips to observe the proceedings.
"I am in discussions with an established London law firm and two senior barristers," he said.
"We believe there are loopholes in the Benn Act that we can take to court, to try to test the legislation.
"The Benn Act is a rag-bag, badly drawn up piece of legislation, it never faced proper scrutiny.
"Ironically, there are areas of European Union laws that govern international negotiations between EU countries under which we might be able to take it to court."
The European (Withdrawal) (No. 2) Act, sponsored by Hilary Benn, requires the Prime Minister to write to the EU asking for a further delay to Brexit by October 19 unless parliament has approved either a deal or a no-deal Brexit. Given that there is not a parliamentary majority for leaving without a deal, it would mean that Britain could not leave unless MPs back a deal.
Mr Kawczynski said he took the idea from Remain campaigners who had used the courts to further their cause.
"I saw how the Remainers had used the courts in trying to block the centuries-old prorogation traditions."
He said his biggest difficulty would be securing the funds for a legal fight, but was confident that funds would be available.
"If the lawyers advise me there is a possibility of going to court, there will be sources of funding we can apply for," he added.
"We must not allow our opponents to bind the hands of PM as he negotiates with overseas power.
"We need to deliver Brexit by October otherwise British democracy will be tarnished for future generations."
There has also been speculation that Mr Johnson might ask European leaders to insist on Britain leaving on October 31 as part of any deal, effectively negating the Benn Act.