The club have also made a formal approach to the United States Soccer Federation as they move closer to appointing the Argentine.
Manchester United's chief executive Omar Berrada and director of football Jason Wilcox returned from Monaco after discussions involving minority owner Sir Jim Ratcliffe, with Carrick's future expected to be central to the meeting. The club are preparing to part company with the former midfielder, although the timing of an official announcement remained uncertain.
Pochettino is currently in charge of the United States national team and has been preparing for a CONCACAF Nations League quarter-final double-header against Haiti. He was still overseeing training on Wednesday, while Carrick also reported for work at United's Carrington training ground as the situation developed.
The agreement with Pochettino is understood to be in place on the condition that Carrick is removed. The 54-year-old has previously managed Southampton, Tottenham Hotspur and Chelsea, giving him extensive experience of the Premier League.
United are prepared to meet the cost of releasing him from his contract with US Soccer. Pochettino signed a new agreement following the World Cup, committing himself to the national team until 2030, but his contract is understood to include a release clause worth approximately £7 million.
The overall cost of the appointment would be higher once compensation for his backroom staff is included. Trusted assistants Jesus Perez and Miguel D'Agostino are expected to be part of his team, taking the potential financial commitment beyond £10 million.
The timing of the move remains complicated by the United States' international commitments. The Americans are due to face Haiti in the first leg in Kingston, Jamaica, before the return match in Cincinnati the following week.
United are understood to be relaxed about Pochettino remaining with the national team for at least the first fixture. He could then travel to Manchester, although the possibility of him taking charge only on Friday would leave little time to prepare for United's next major assignment, an away match against Liverpool at Anfield.
US Soccer are understood to have a succession plan in place should Pochettino leave. The federation also cancelled planned media access to its players on Wednesday, although sources attributed the decision to Veterans Day rather than the uncertainty surrounding the coach's future.
Bournemouth midfielder Tyler Adams, who is part of the United States squad, was asked about the possibility of his manager taking the United job. He responded: "Why would his name not be on it? I mean, the credibility, the resume speaks for itself. It goes to show for us how lucky we are to be able to work under a manager of his quality and the person he is."
Pochettino's potential arrival would end Carrick's tenure after a difficult start to the season. United have struggled for consistency and entered the international break in the relegation zone, leaving the hierarchy facing a major decision.
The club's immediate priority is to finalise Carrick's departure and complete the arrangements with US Soccer. Although Pochettino's verbal agreement represents a significant step, his appointment is not official until the remaining formalities have been completed.