Watson did not feature in the first Test in Brisbane after succumbing to a calf strain he sustained while bowling for New South Wales in a Sheffield Shield match just days before the series opener.
The 31-year-old confirmed on Monday he could not bowl if selected and would concentrate on proving his fitness as a batsman.
The bustling all-rounder trained in the nets on Tuesday before he was put through a number of fitness exercises and tests.
Ponting said Watson looked comfortable while batting but was restricted to slips catching when it came to fielding drills.
The former Test skipper reaffirmed that Watson would not receive a late recall if he was struggling before Thursday's start, suggesting his selection would heap greater pressure on the Australian side.
"No one can go into a Test match 70 per cent fit. I don't care if you're a batsman and a slip fielder. If you can't bat at 100 per cent, then you are putting pressure on other blokes as well," Ponting said.
"It doesn't matter what we think as teammates, he will have a certain lot of criteria he will have to pass.
"There will be a certain amount of running he will have to do along with other things to prove that he's right to play a Test match.
"Someone has got to run with him between wickets and I'm sure that will be in the back of his mind - and certainly in the back of the mind of our physio and doctors - that are looking after him for the next couple of days.
"I believe he did some extra running last night and I'm not sure if he is planning to do that today but they will tick all the boxes to make sure he's right to play."
A decision on Watson will be made on Wednesday or the Thursday morning of the five-day clash, although Rob Quiney - who made his Test debut in Brisbane - is expected to retain his spot at number three.
Another selection dilemma Australia face is whether to drop paceman Ben Hilfenhaus for left-arm quick Mitchell Starc.
Starc, who carried the drinks in the drawn opener, is favoured to replace Hilfenhaus after the Tasmanian bowler failed to have an effect at the Gabba, taking just two wickets across both innings.
Starc pushed his claims for a fifth Test cap after taking four wickets for New South Wales in their four-day fixture against Victoria last week.
Ponting had high praise for Starc, and said he will provide selectors with a headache when picking the bowling line-up this week.
"I've been impressed with Mitchell and his development in all forms of the game over the last 12 months," Ponting said.
"What he's done for Australia in one-day cricket in particular has been pretty spectacular and we just hope that he keeps developing that way as far as his red ball cricket is concerned.
"I've faced him both days in the nets and he's been pretty good.
"When you've got a left-armer who can bowl at his pace and swing the ball back, it makes for a very dangerous proposition for any batsman.
"There's going to be a tough decision to be made whichever one of the quicks happens to miss out, but I'm sure the selectors, captain and coach will pick the four bowlers they think are the best chance to take 20 wickets in the game."
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