The 31-year-old Tasmanian allrounder hit the winning runs on debut against India at the SCG as Australia clinched the Border-Gavaskar Trophy with a 3-1 series triumph.
Selectors will this week name the touring party for two Tests against Sri Lanka in Galle, beginning on January 29.
Skipper Pat Cummins is likely to miss both matches because of the imminent birth of his second child, and spin-friendly decks will almost certainly result in a tweaking of the bowling attack.
Webster sent down 17 overs of pace in the fifth Test against India and picked up one wicket to go with his 96 runs across two innings.
He believes his rise to the highest level is because of his development as a seam bowler.
However, he still has offspin in his kit bag, with his two bowling options once used in one over in the Big Bash League.
Webster said his skill-set could prove an asset in subcontinental conditions.
"The offies don't get wheeled out as much as they used to - more seam-friendly conditions in Australia," he said.
"I've tried to work really hard on them (pace deliveries) to become a genuine allrounder.
"But I've still bowled offspin in first-class cricket this season and I bowled it in the (Sheffield) Shield final last year. If the conditions suit it, they are still there."
Beau Webster arranging his long limbs while bowling offspin for Tasmania in the Sheffield Shield. (Kelly Barnes/AAP PHOTOS)
Colin Miller once filled a similar role for Australia through 18 Tests in the late 1990s and early 2000s with his combination of seam-up and offspin.
Retired Test spinner Steve O'Keefe said picking Webster to do the same would help Australia be ready for any kind of pitch prepared in Sri Lanka.
"When (Webster) first started out he bowled offspin and they were handy," the nine-time Test player told AAP.
"What a great luxury you could have, picking a guy at six who can bowl some handy medium pace, and if the wicket is an absolute dust bowl and you do need that extra (spin) option, you've got two guys, Travis Head and himself."
Head memorably took 4-10 with his part-time offspin in the second innings of Australia's 10-wicket win in Galle on the last tour of Sri Lanka.
With Australia a chance of picking as many as three front-line spinners in Galle, O'Keefe said Webster and Head would likely only be called on to bowl spin in case of emergency.
"You'd be relying heavily on your main spinners, and if those guys do get an opportunity to bowl, I think it'd be because something's gone wrong," he said.
"If you're picking three spinners, you're probably a little bit desperate if you're turning to him."
Regardless, Webster has his eyes on a second Test cap in Sri Lanka.
"I'm really hoping I am in that (Sri Lanka) squad," Webster said.
"It is (also) a part of my game I've worked really hard on, playing spin bowling.
"And there is no bigger challenge than playing in the subcontinent. I'll adapt my game … if I am on the plane."
Webster arrived back in Hobart on Monday afternoon to multiple television crews and an impromptu press conference.
His baggy green was tucked away in his backpack and "still wet" from post-Test celebrations featuring Carlton Draught.
Webster said he planned to have a few days' rest before returning to play in the BBL with the Melbourne Stars.
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