The 34-year-old had looked set to leave Old Trafford this summer, with his current terms expiring at the end of June.
Back in February, The Express claimed Arsenal, Newcastle and several Chinese Super League clubs were all in contention to sign the England international on a free transfer.
But according to The Daily Mail, fresh managerial appointment Jose Mourinho has told Carrick he wants him to stay on at United for his first season at the helm.
The Red Devils are now expected to thrash out a one-year contract extension with the midfield maestro by the end of next week – taking his Old Trafford tenure to an eleventh season.
During 421 appearances for the Carrington outfit, Carrick has lifted five Premier League titles, the 2008 Champions League title, one League Cup and one FA Cup.