Last week's loss at Edgbaston was Clarke's 12th Test defeat overseas as skipper.
Clarke has dug in his heels, saying he is confident the wheel will turn and he has no interest in retiring after the five-Test series.
"I wouldn't (hope there'd) be any knee-jerk reactions on his situation," Border told cricket.com.au.
"He'll know himself if he wants to keep going and if he's got the hunger for it.
"He looks like he's under pressure, but that's understandable with his circumstances and the team's circumstances."
Australia have a two-Test tour of Bangladesh in October then host New Zealand and the West Indies in three-Test series.
Border felt the time was wrong for Clarke to hang up the boots.
"It hasn't quite worked out and I understand all that, but I don't think we're ready for that change just yet unless he thinks it's time," Border said.
"He deserves the opportunity to go out on his own terms.
"He wants to perform well. He's a very passionate bloke, he works hard at his game."
Border captained Australia in 93 Tests, more than any other man.
The 60-year-old is also a former selector.
-AAP