Manchester United dismissed Rúben Amorim in early January following a run of poor results and turned to Carrick as interim head coach. The 44-year-old former midfielder, who had been sacked by Middlesbrough the previous summer, returned to Old Trafford on January 13 to take charge until the end of the campaign.
The turnaround under Carrick has been striking. United have won ten of his 14 Premier League matches in charge, losing just two, and recorded wins over Manchester City, Arsenal, Aston Villa and Liverpool along the way.
Sunday's 3-2 victory over Liverpool at Old Trafford was the result that confirmed a top-five finish, sealing Champions League qualification for next season and ending a two-year absence from Europe's top competition. Kobbie Mainoo scored the decisive goal.
United now sit third in the table after 35 rounds, six points ahead of Liverpool in fourth.
The Guardian reports that a formal offer to Carrick is expected imminently, with the decision now his to accept or decline. Football director Jason Wilcox and chief executive Omar Berrada are said to be impressed with his impact, and no formal talks have yet taken place between the two parties.
Fabrizio Romano has described Carrick as the clear favourite internally, with the club understood to have been waiting for Champions League qualification before committing.
Several senior players have also made their preference known. Bruno Fernandes, Harry Maguire and Matheus Cunha have each told club hierarchy they want Carrick confirmed as permanent manager.
United's remaining fixtures are against Sunderland, Nottingham Forest and Brighton and Hove Albion.