"We welcome the changes your administration has made in recent days in how the Department of Homeland Security will implement the Executive Order," according to a draft of the letter.
The technology companies expected to sign the letter include Apple Inc, Facebook Inc, Alphabet Inc's Google, Twitter Inc, Microsoft Corp and Yahoo Inc.
The sources did not want to be identified because discussions regarding the letter were ongoing.
On Jan. 27, Trump issued an executive order imposing a 90-day ban affecting citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen and a 120-day bar on all refugees. Those travel bans caused chaos by trapping some travelers at airports and stranding others overseas.
A federal judge on Friday put a temporary nationwide block on that week-old executive order, leading the Republican president to criticize the judge and the court system.