The Scot has indicated he will not shy away from any potential duels with the Portuguese following recent remarks by the Chelsea boss about transfer target Wayne Rooney
The Portuguese fell out with several Premier League rivals during his previous spell at Stamford Bridge, including the likes of Arsene Wenger and Rafael Benitez.
But, when questioned on the topic by a fellow Scot after United's pre-season victory over the A-League All-Stars, Moyes denied he would be overwhelmed by Mourinho's charismatic style.
"It sounds like your accent's like mine, and if you're from Glasgow then you enjoy those sorts of things, so bring it on," Moyes said at a press conference.
Meanwhile, the 40-year-old admitted there had been little development on the transfer front, despite the club's chief executive, Ed Woodward, flying home on "urgent transfer business."
"I've not had any more news since we last spoke yesterday," Moyes continued.
"I have no more updates so I couldn't give you anything positive or negative."