Morris had been part of Australia's squad for the majority of the home summer, before the West Australian earned his spot in a touring party for this year's series in India.
"He's having a bit of a de-load period, which I think is about four-to-six weeks, and then he will start to start to build after that," chief selector George Bailey said. "Conservatively, we'll probably look to rebuild Lance and hopefully have a really big crack at the summer.
"He'll get another scan in four-to-six weeks and we'll get a better indication of of how that back's going."
Hazlewood is returning from two lengthy injury lay-offs in the IPL, with the seamer in constant conversation with Australian medical staff on building up his workload outside of games.
There are three short turnarounds throughout the England tour, with Bailey noting it was hard to determine if bowlers would be managed until it was clear how quick matches were completed.
"If we do need to call upon another quick we can we can be really specific around who we need and why," Bailey said. "And then not necessarily have someone in the squad who ends up being superfluous."