The injury-plagued seamer has played only two tests in the last 15 months and was left out of the squad which beat India in the World Test Championship (WTC) final at The Oval on Sunday.
Australia now have a selection headache before the five-test series against England with Scott Boland, Mitchell Starc and Hazlewood vying for two slots in a pace attack spearheaded by skipper Pat Cummins.
Hazlewood acknowledged he would have found it difficult to play the WTC final and all five Ashes tests on the condensed tour given his injury issues over the last couple of years.
"If we go back a few years, I would have said all six," Hazlewood told reporters on Tuesday when asked how many matches he would have liked to play on the tour.
"But I guess it's a little bit different now, based on the last two years. Three would be a nice pass and four is probably a tick.
"Any more than that is great, any less, then I am probably a little disappointed again."
Boland was the most impressive Australia bowler in the WTC final with former captain Aaron Finch and retired speedster Brett Lee calling for the Victorian to be retained in Edgbaston.
Hazlewood did not believe Boland's rise posed a threat to his place in the side.
"When you have that depth ... you really go as hard as you can and then reassess after the game," Hazlewood said.
"You always have someone of high quality sitting on the pine and ready to go."
The emergence of Boland and seam-bowling all-rounder Cameron Green could actually help prolong his career, he added.
"You might miss one or two games with a niggle now, rather than pushing it and missing three or four months.
"We probably played 20 or 30 tests with no all-rounder, and that was pretty tough yards for a few years.
"If we have a group of four or five quicks we can go together for longer," he added.
