Shane Warne's Australia record 708 Test wickets and Glenn McGrath's next-best 563 are set to prove far beyond the reach of the 33-year-old left-arm quick.
But the Test tallies of fellow Australia fast bowlers Brett Lee (310) and Lillee (355) are within range for Johnson.
Last week, Australia lost the third Test at Edgbaston by eight wickets as England took a 2-1 lead in the five-match Ashes series.
One consolation for Johnson was the manner in which he got to 300 Test wickets, a rip-snorting bouncer which England's Jonny Bairstow gloved to wicket-keeper Peter Nevill.
"It was a very special occasion," Johnson said Tuesday of the delivery that did for Bairstow.
"And the way I did it. I guess that's sort of a trademark for me now, to bowl that short ball and get it ripping off the gloves," he also told reporters at Trent Bridge, where the fourth Test starts tomorrow.
"The next target for me is trying to chase down Brett Lee. That'd be really nice, he's a hero of mine," Johnson added.
But it was Lillee who first alerted Australia's hierarchy to Johnson's talent, having coming across the then teenage paceman in his role as a fast-bowling coach.
Lillee has remained a source of support and Johnson said: "It would be nice to reach DK Lillee. That'd be pretty special.
"You never know, if I get that opportunity to reach him and could end it there as well. It would be a nice little finish as well. It's probably something I don't normally think about.
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