Brad Haddin, 36, who took 29 catches on the Ashes tour for a new world record, has reclaimed his status as Australia's first-choice gloveman.
But his successor, who could be called upon sooner rather than later, is likely to be one of the two Hobart-born glovemen.
"I don't think we've, as a selection panel, tried to rank one over the other," Inverarity said.
"Matthew's form with the gloves in England wasn't what it might have been, so we've gone very much with Brad there and it's up to them now to compete hard to see who will be the next keeper.
"(Paine) has now regained confidence after the nasty injury to his finger, and he's playing well, his keeping at the end of last season and the Ryobi Cup was very good."
Paine won the Sheffield Shield final last season with Tasmania, including a second innings dig of 87 after coming in at 5-15.
"When the hard decision comes, we'll do the best we can to in trying to determine which one it is," said Inverarity.
Paine, 28, will turn out for Australia A against England in Hobart next week while Wade, 25, captains his adopted state of Victoria.