The 19-year-old has joined the reserve team ranks at Ewood Park after coming through the Sandgrounders youth system.
"We're hoping for him to play in the Premier League in the next 18 months," Reece told BBC Radio Merseyside.
"To sign for Blackburn is a tremendous achievement for Zac. Hopefully he's on the ladder to international stardom."
He added: "Zac has studied with us as a scholar for the last 18 months. He's achieved his BTec's and his NVQ's and he's a qualified referee now and he's on the ladder of FA coaching badges."