The Portuguese has been perceived to be engaging in mind-games over the Blues' summer pursuit of Wayne Rooney, with his latest statement suggesting that Chelsea would not have to sell anyone in order to buy the England striker.
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"Jose Mourinho is a tremendous manager," Moyes told reporters. "He has done really well in the Premier League.
"Like me, he started doing his coaching badges in Scotland and, whilst I wouldn't say I know him that well, I do know him."
The Scot also revealed that his admiration for Mourinho went so far that he wrote the Portuguese a letter after his first spell as Chelsea boss ended in 2008.
"I remember when he lost his job I wrote him a letter," he explained, "so for people to say there is any feud is wrong.
"Of course, you are going to find two really competitive managers. When our teams play we will both be highly committed to make sure our clubs win but I admire him for how well he has done as a manager."