According to the Daily Star, the United boss is a big fan of Ramsey’s all-action style.
And he’s said to be 'weighing up' a swoop for the 27-year-old at the end of the season.
Mourinho’s reported interest in Ramsey comes as his dissatisfaction with Paul Pogba grows.
The Daily Star claim Mourinho has said Pogba and Alexis Sanchez are "killing the team."
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Manchester United could fight Chelsea for Arsenal midfielder Aaron Ramsey in the summer
Arsenal stars astonished as Aaron Ramsey beats THE CUBE
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Manchester United boss Jose Mourinho is a fan of Arsenal's box-to-box midfielder Aaron Ramsey
United will have a fight on their hands if they do make a move for Ramsey in the summer.
Chelsea are eyeing up the Caerphilly-born Arsenal ace as they look to bolster their squad.
Mourinho, meanwhile, is planning to axe as many as eight United players, including Zlatan Ibrahimovic.
Luke Shaw, Juan Mata, Ander Herrera, Chris Smalling, Phil Jones, Daley Blind and Matteo Darmian are set for the chop too.