However Arthur, who is part of the five-man selection panel, has hinted Cowan will stay to open with David Warner, should Warner prove he has recovered from a fractured thumb which kept him out of the one-day series against West Indies earlier this month.
"We just want to see how Davey Warner comes up over the next day or two," Arthur told reporters on Tuesday in Chennai.
"It's critical that he trains well over the next day or two to play.
"I'm pretty sure and confident he'll come through but he hasn't faced any quicks yet."
Cowan has shown solid form with scores of 58, 40 and 53 in Australia's tour matches against the India Board XI and India A, while Watson dominated last weekend's three-day game with scores of 84 and 60 in two century stands with Cowan.
Watson's most recent Test appearance was in Melbourne against Sri Lanka in December at No.4 before missing the Sydney Test with a calf injury.
The vice-captain has said he is expecting to bat at No.4 against India if Warner is fit.
"It's a little bit difficult to give that away right now. Let's first see how Dave comes about and then we'll attack that conundrum," Arthur said.
"Ed has come out of these practice games with his head held high.
"He's had a good method against the spin and he's played exceptionally well.
"That would be a tough call but that's something we have to only weigh up once Davey Warner is fit or not fit."
Arthur says Watson was a class player wherever he batted in the top six.
"Potentially through the middle is going to be a real tough time to bat so you want your most seasoned campaigners in that area," Arthur said.
"Plus you want a guy that can take the spinners down. There is no point in us defending.
"I do think though that we've just come off a series where we've been Sri Lanka 3-0 in our last Test series and do those players get first opportunity? I don't know."