Authorities in New York, Washington DC and Los Angeles have ramped up their law enforcement presence.
A Manhattan prosecutor may charge Mr Trump over how he declared a payment to a porn star to keep quiet about an alleged affair.
It would be the first criminal case brought against a former US president.
Steel barricades were erected on Monday outside the prosecutor’s office and the Manhattan Criminal Court, where Mr Trump could be charged, fingerprinted and photographed if charges are filed this week, as US media widely anticipate.
Increased police presence and barricades have also been seen outside Manhattan’s Trump Tower.
Every member of the New York Police Department (NYPD), including plainclothes detectives, has been ordered to wear their full uniform on Tuesday and is being placed on standby to mobilise.
As of Tuesday morning, however, dozens of camera crews and reporters had taken over city sidewalks in the vicinity of the courthouse, outnumbering by far the handful of demonstrators who had shown up to voice their opinions on the potential indictment.
The US Capitol Police, who protect lawmakers on Capitol Hill in Washington DC, has deployed bike rack fencing around the perimeter of the Capitol complex and will beef up staffing.
The Capitol Police plan to issue an emergency declaration on Tuesday, a congressional source told CBS. The order aims to increase co-ordination with other law enforcement agencies.
More civil disturbance officers will also be on standby, though the congressional source said there was no specific threat and that the order was proactive.
In Los Angeles, the LAPD and federal officials were preparing for a pro-Trump protest on Tuesday outside a federal building, the LA Times newspaper reports.
In a post on his Truth Social platform on Saturday, Mr Trump said he expected to be arrested on Tuesday and urged his supporters to protest against the authorities if he is detained and indicted.
He published a long statement describing the investigation as a “political witch-hunt trying to take down the leading candidate, by far, in the Republican Party”.
However, it’s worth noting a spokesperson for Mr Trump said he had not been notified of any pending arrest.
The case – that the Republican made a payment to Ms Daniels towards the end of the 2016 presidential campaign in exchange for her silence over an alleged affair – is one of several related to Mr Trump.
Other ongoing cases include a Georgia election interference probe and two federal investigations into his role in the 6 January insurrection in the US Capitol.