"He's amazing," Arquette said of the Snow Patrol rocker. "Great guy."
Arquette, 42, finalized his divorce from Cox, 49, in May 2013 after 13 years of marriage, and shares custody of 9-year-old daughter Coco. The Cougar Town actress was first romantically linked to 37-year-old Irish musician McDaid back in December. The couple were photographed enjoying a vacation to Venice, Italy on Feb. 17, and bonding with Coco over an ice cream treat.
Are Cox and McDaid talking marriage? "I don't know," Arquette told host Wendy Williams with a laugh. "We've gone out to dinner a few times. My whole thing is that, he's a great man and to have someone kind, that you trust around your kid is the most important part."
"She's an amazing mother and a dear friend," Arquette added of his ex-wife. "We are great co-parenters together."
The actor, who currently stars in Lifetime's TV thriller Happy Face Killer, is expecting his second child, a baby boy, with girlfriend of two years, Entertainment Tonight correspondent Christina McLarty.
Arquette told Williams that daughter Coco is excited to welcome a baby brother -- under one condition.
"She was like, 'I'm going to be fine with it as long as he worships me,'" he recalled his daughter telling him. "She actually said that."