Wade has been the first choice keeper since winning his spot behind the stumps back from Peter Nevill in 2015/16 Australian summer.
However, he has struggled with the bat and the gloves of late, prompting Border to question his spot in the XI.
“I think Matty Wade’s position in the side is another question mark,” Border said on Fox Sports News.
“He really struggled behind the stumps, which is his key role, and again with the bat.
“So they may look at putting Handscomb in as the wicketkeeper and playing an extra batsman.
“I thought (Wade’s) keeping was improving, but once you go to the subcontinent you really test your skills out there.
“It’s difficult, but 30 byes in that last Test match was pretty telling, wasn’t it?
“He’s not producing enough runs with the bat to compensate for the keeping. So he’s the one under the most pressure.”
However, Border said if Handscomb if thrown behind the stumps, it would only be a short term fix.
Wade scored five and four in his two innings against Bangladesh in the first Test.