Watson, a regular in the world champions' one-day side, has only played three Tests but would provide an extra bowling option for captain Ricky Ponting, particularly with doubts over the fitness of veteran seamer Glenn McGrath.
"He's (Watson) the guy that we're looking at very closely," Border told reporters.
"He's got the early running there's no doubt but that's not to say someone might not come out of the woodwork.
"If he can get in there with both bat and ball that's the ideal scenario. It makes the balance of the side a lot better."
The 25-year-old Watson played in the tri-nations one-day tournament in Malaysia this month after proving his recovery from the injury problems that plagued him last season.
"It would be fantastic if we can unearth that quality of all-rounder other countries have had recently," Border said.
Watson would probably bat at number six in the Australian order, meaning the likely omission of young batsman Michael Clarke or the experienced Damien Martyn.
