Harare-born Ballance moved to England as a schoolboy and played 23 Tests and 16 one-day internationals before falling out of favour.
The 32-year-old has not played for England since a 2017 Test at Nottingham and recently apologised for using racist language against former Yorkshire team mate Azeem Rafiq.
Houghton said his wife and Ballance’s father were cousins.
“I’ve known Gary since he was a kid and I speak to him reasonable regularly,” the former captain told reporters ahead of the team’s second one-day match against Australia on Wednesday.
“I don’t think Gary would be against coming back to play for Zimbabwe but he’s still got to sort out things in England.
“I think he’s probably got another eight to nine good years in him, so if he wants to come back we certainly won’t turn him away.”
Australia coasted to a five-wicket victory in the first one-dyer on Saturday with 16.3 overs to spare.
Zimbabwe have been boosted by the return of all-rounder Sean Williamswho missed the opener with an elbow bruise suffered in the nets.