The 19-year-old quick took seven wickets in a remarkable test debut in South Africa in October 2011 but has been unable to pull on the baggy green cap again because of a succession of injuries.
The latest problem, a strain to his upper back sustained in the Twenty20 Champions League last October, forced him to miss the rest of the domestic summer and his return still looks some way away.
With Inverarity saying the selection of the squad for the England trip was at "an advanced stage", Cummins will now have to look to the second Ashes series of the year, starting back in Australia in November, for his test return.
England and Australia are playing back-to-back Ashes series this year to move the series out of its position directly ahead of the World Cup in the international cricket calendar.
"He's tracking well, the one thing we're certainly not going to do is rush him," Inverarity told reporters in Perth on Wednesday.
"He's working on three fronts. Firstly, he's working on rehabilitating his back injury and the second thing is he's doing a lot of strength and conditioning and fitness work.
"The third thing, which he's doing a lot of work with Dennis Lillee on, is remodelling his action because his action had a lot of twists and turns in it."
Cummins, who comes from the rural Blue Mountains to the west of Sydney, burst onto the test scene in 2011 when he took six for 79 in the second innings at Wanderers to help Australia to a two-wicket victory.
Seen by many as the future leader of Australia's pace attack, he had already become the youngest player to be awarded a central contract by Cricket Australia in June 2011, just three months after his first class debut.
On Wednesday, he was included on the list of 20 players awarded central contracts for 2013-14 - a sign of his continued importance to the future of Australian cricket.
Having spent much of last year dealing with a lengthy injury list of pace bowlers, however, the Australian selectors are in no hurry to unwrap the cotton wool.
"He's a question mark in terms of when we bring him back," Inverarity added. "When he comes through, we want him to come through without any further mishap."
- Sports & Recreation