The spending bill has already passed in the House of Representatives, but needs 60 Senate votes to advance.
Among the changes Democrats are seeking are requirements that federal agents obtain warrants before making arrests and clearer rules governing how they identify themselves, according to US media reports.
There are only 53 Republican senators in the 100-member body, meaning that passing the bill will require at least some support from Democratic members.
Earlier this week, Senate Minority Leader Chuck Schumer said: “I will vote no on any legislation that funds ICE until it is reined in and overhauled, and Senate Democrats are overwhelmingly united on this issue.”
Republican Senate Majority Leader John Thune has said that “productive” negotiations are ongoing.
If changes are made, the bill will need to be re-approved by the House, which is currently on recess.
On Wednesday, some Senate Democrats escalated their demands, expressly calling for DHS Secretary Kristi Noem’s removal, and structural changes to both Immigration and Customs Enforcement (ICE) and US Border Patrol.
“This madness,” Schumer said, “this terror must stop.”
Some Republicans pushed back, with Texas’s John Cornyn saying that “any changes must not come at the expense of shutting down the government”.