The meeting is being called together by GitHub, which makes software development tools.
Amicus, or friend of the court, briefs are filed by parties who are not litigants in a case but want to offer arguments or information to the judge.
Alphabet Inc's Google, Airbnb Inc and Netflix Inc are among the companies invited, a separate person familiar with the situation said.
Representatives for Google and Netflix could not immediately be reached for comment. An Airbnb spokesman declined to comment.
The technology sector has become the clearest corporate opponent to the ban announced last week. The industry depends on talent from around the world, and companies have been considering the best way to muster their resources, with efforts so far including statements condemning the move and financial support for organizations backing immigrants, such as the American Civil Liberties Union.
The Trump administration says the rules will increase national safety and are well within its powers.
Michal Rosenn, general counsel for fundraising company Kickstarter, which will be involved in a filing, said the effort began on Monday.
"We're all very shaken. We're shaken to see our neighbors and our families and our friends targeted in this way," Rosenn said. "All of us are trying to think about what we can do."
The discussions among the tech companies come after Amazon.com Inc and Expedia Inc filed declarations in court on Monday supporting a lawsuit filed by the Washington state attorney general. Amazon and Expedia said Trump's order adversely impacts their business.
A separate lawsuit challenging Trump's order as unconstitutional was filed on Monday by the Council on American-Islamic Relations. If the tech companies decide to file an amicus brief as a group, it is unclear which case they would weigh in on.
Other companies invited to meet include Adobe Systems Inc , AdRoll, Automattic Inc, Box Inc, Cloudera Inc, Cloudflare Inc, Docusign, Dropbox, Etsy Inc, Evernote Corp, Glu Mobile Inc, Lithium, Medium, Mozilla, Pinterest, reddit, Salesforce.com Inc, SpaceX, Stripe, Yelp Inc , and Zynga Inc, the source said.
A representative for internet communications company Twilio confirmed it will be involved in filing an amicus brief.
Cloudflare Chief Executive Matthew Prince said the internet security company is willing to consider and sign an amicus brief. Denelle Dixon, chief legal and business officer for Mozilla, said the immigration order was "misplaced and damaging, to Mozilla, to the technology industry and to the country."
Spokespeople for Box and AdRoll said they would attend the meeting. An Etsy spokeswoman said the company received Github's invite but could not confirm if it would move forward with the group.
Salesforce declined to comment. Representatives for the other companies could not immediately be reached for comment.