The news was first reported by The Athletic.
Tillman, 24, was born in Germany to a German mother and American father and previously represented the country of his birth at Under-15 through Under-19 level. He is the older brother of Malik Tillman, who made his debut for the USMNT in June 2022.
The former Bayern Munich youth product has made an impressive start to life in Los Angeles since signing for the MLS Cup holders from 2. Bundesliga side Greuther Furth ahead of the 2023 season. He has two goals in seven MLS appearances and also scored in LAFC's CONCACAF Champions League semifinal win over Philadelphia Union last week.
His proposed switch represents the latest success for the U.S. in recruiting dual nationals to its program.
Defender Sergino Dest, currently on loan at AC Milan from Barcelona, Valencia midfielder Yunus Musah and Club America's Alejandro Zendejas are among those who have declared their allegiance to the U.S. in recent years.
Tillman's switch comes amid a period of uncertainty for the USMNT, which is still without a permanent coach following the expiration of Gregg Berhalter's contract at the end of 2022.
While Anthony Hudson remains in temporary charge, U.S. Soccer last month announced the appointment of sporting director Matt Crocker, who will lead the search for a coach to take the men's team into the 2026 World Cup on home soil.
If Tillman's switch is approved, he could be in contention to feature for the team this summer, when it faces both a semifinal and potential final of the CONCACAF Nations League as well as the Gold Cup tournament.
Information from ESPN's Kyle Bonagura contributed to this report.