Zajac and McLeod have both been medically cleared to practice with the team.
Zajac, who underwent surgery to repair a torn left pectoral muscle on Aug. 17, was happy to be out on the ice with his teammates.
"We've had an internal timeline and we're pretty much on schedule," Zajac said. "It was exciting to be out there with the guys, skating and shooting on goalies."
Coach John Hynes said Zajac will take part in his first road trip of the season starting Thursday in Toronto.
"He's cleared to play," Hynes confirmed. "So he's got to practice a little bit. He's not going to play this weekend, but I would anticipate early next week."
Zajac added: "I've been skating a while, just not with the guys. It's more just now getting in some practices where I can skate through some bodies and bump a little bit. The next week will be important to me."
The Devils wrap up a three-game home stand Saturday night. They look to snap a four-game winless streak, as they host the Florida Panthers. Florida is coming off a 4-1 win over the Sabres in Buffalo on Friday night.