The borders between Iraq and Syria will not be turned into a safe zone anytime soon. This will be subject to major negotiations between the two concerned countries, as well as between the United States and Iran.
The United States seeks to ward off all threats against its military base in al-Tanf and keep away all forces from the borders, except for the forces it backs.
Iran also wants its allied forces to take care of the Iraqi-Syrian border issue because it still wants to open a land crossing linking Iraqi-Iranian borders in eastern Iraq to the Iraqi-Syrian border in western Iraq. This issue that Washington and Tehran have been fighting over will place Abadi in an embarrassing position.
Abadi does not want to anger or marginalize the PMU, but he also does not want to lose his US ally, as he seeks to prevent the PMU from having the last say on the border issue.
A military conflict over the Iraqi-Syrian border between the allies of Tehran and those of Washington is on hold now because of the ongoing military operations in Mosul.
However, it seems this conflict is inevitable and likely to erupt after the liberation of the district of Tal Afar in the Ninevah governorate.