The Manchester United midfielder is out of contract at the end of the season and currently pockets around £130,000 a week.
But The Sun claim Old Trafford chiefs want Carrick to accept wages of £70,000 a week.
A United source told the paper: “Carrick could be asked to take a reduction to his salary to secure another deal.
Michael Carrick is out of contract at the end of the season
Mourinho out! Man United fans furious after Hull stalemate
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“He wants to stay and by all accounts Jose has told the board similar. He is on big wages here and would have to take a cut.
“Carrick’s influence and experience in United’s engine room is undeniable, he’s a key player for the team."
Jose Mourinho is keen to keep hold of Michael Carrick for an extra season
Old Trafford chiefs want Michael Carrick to take a pay cut
Jose Mourinho has made it clear to United bosses he would like the 35-year-old to stay on another season and the board are keen to respect his wishes, providing the former England international agrees to a smaller salary.
The report claims Ryan Giggs, Paul Scholes and Rio Ferdinand all had to take pay cuts in their final few years at Old Trafford and United hope Carrick will follow suit.