Mourinho has irritated Moyes by openly stating his interest in signing Manchester United striker Wayne Rooney.
When both clubs were in Bangkok at the start of their pre-season tours of the Far East Mourinho claimed discussion of other club's players was off-limits - only then to say he would be a "hypocrite" if he denied he was a fan of the England international.
That led to talk of mind games between the two managers, which Moyes fuelled when he said "bring it on".
But Moyes insists there is no conflict between the pair, beyond what normally exists between competing managers, and that they have always got along.
"Jose Mourinho is a tremendous manager," said Moyes. "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."
And Moyes revealed he offered his sympathies after Mourinho's exit from Chelsea in 2008.
"I remember when he lost his job I wrote him a letter," he said. "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."