The 21-year-old Renshaw has averaged 36.64 from his 10 tests in a positive start to his international career but has had a tough Shield campaign for Queensland, failing to surpass 20 runs in his four innings.
Neither coach Darren Lehmann nor any of Australia's other selectors have queried the youngster's spot in the test side but his poor run of form has attracted plenty of scrutiny from local media in the leadup to the Gabba test starting Nov. 23.
Warner will be on the opposite side when Renshaw pads up against New South Wales at Brisbane's Adelaide Border field from Tuesday but wished the opener well.
"I want him to score runs this week. He's been under a bit of pressure this week, there's been a bit of talk in the media," Warner told local media on Sunday.
"You have to keep putting the numbers on the board.
"As a youngster I would be steering clear of newspapers this week."
Renshaw's task has been made easier, with New South Wales resting their trio of test bowlers, Mitchell Starc, Josh Hazlewood and Pat Cummins, who were superb in defeating Western Australia in the previous round.
Renshaw enjoyed a fine home summer against South Africa and Pakistan, but since stroking 60 against India in Bengaluru in March, he has not scored a half-century in nine test innings.
"I want him to do well. I am a mate of his and wish him success," Warner said.
"He's got to keep playing well.
"When I see that at the other end it brings a spark to my eye because you know your partner is on as well."
Halfway across the country, England's crushing 192-run win over a weak Cricket Australia XI in the tour match in Adelaide came with a warning from former test paceman Ryan Harris.
"I think it is (vulnerable), especially with no Ben Stokes," Harris, who coached the home side, said about the tourists' batting.
England's bowlers performed well in the four-day game but former captain Alastair Cook's lean tour continued with scores of 15 and 32.
"I think (Cook) looked a bit rusty, I guess," added Harris.
"I'm sure he'll look forward to another hit next week. But we all know what he can do. You don't score over 10,000 runs and not be any good."
England play their final warmup match against a Cricket Australia XI in Townsville, in far northern Queensland state, from Wednesday.
(Reporting by Ian Ransom in Melbourne; Editing by Sudipto Ganguly)
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