Failing to return the Ashes has led to the Yorkshireman’s position being discussed, particularly given his batting performances have been somewhat inconsistent.
But Bayliss, who leaves his role after four years following this week’s final Test, says there are no issues.
“He’s not come under question from anyone making any decisions,” Bayliss said. “He’s under no pressure at all.”
On Root’s form with the bat, Bayliss added: “Everyone goes through periods where they don’t score as many runs as they’d like. I think the Australian team have bowled pretty well to him, so we’ll see how things go further down the line.
“From my point of view, he was our premier batter and the Australians always try and target the opposition captain. He’s played well when he’s got starts and I don’t see too many problems.”
Bayliss admits his successor will take over a Test team with plenty of room for improvement.
Bayliss’s place in the history books is already assured as the man who oversaw the country’s first World Cup success earlier this summer, but the dream of signing off with an Ashes victory will not be realised.
Defeat at Old Trafford in the fourth Test means his native Australia will be lifting the urn regardless of what happens in his final match at The Oval, though victory would allow him to walk away with a 2-2 series draw.
The world-beating overhaul of England’s limited-overs side will go down as his crowning achievement but there are serious structural questions that remain unanswered in the red-ball format.
Asked to mark himself out of 10, Bayliss said: “I’m a hard marker, so I’ll say five.
“I always gave the guys four, five or six out of 10 for their fielding, because I always thought there was always room for improvement. Our Test cricket hasn’t gone as well as we would have liked. I’d say it’s still a work in progress.
“When you compare the two, the white-ball team had the biggest improvements.
“From a Test win percentage we’re slightly in front on win-loss ratio but the big improvement in the one-day game overshadows the work we’ve tried to do with the Test team.
“From my point of view I like to think I’m a traditionalist, I like the Test match game. I didn’t go easy on planning or coaching the Test team compared to the white-ball team.
“I think we’re further down the track than we were and hopefully the next guy who comes in and takes my place can take the team further.
“Trying to find the depth in our Test ranks, as we have in our one-day ranks, will be a challenge going forward.
“It’s a question that English cricket will have to address and hopefully everyone works together on that and not just throw barbs at one another. Actually get together and work it out together.”
Bayliss has been a low-key figure since his arrival in 2015, preferring to empower players and captains rather than act as a frontman for the team.
It is fitting, then, that he will not use his imminent departure to engineer one last push in a draining summer.
“I said to my wife before I came over, I’d love to win at least one of the trophies this year,” he said.
“When we won the first one, the World Cup, I felt a bit greedy and I would have loved to have gone out on a high. But they owe themselves a performance, not me.
“They owe it to themselves to go out and play well and win this last one.”
Thursday’s match will be the last one where the 56-year-old wears the Three Lions, but he admits future Ashes series will see him facing mixed emotions.
“I’d have to be impartial,” he said.
“Knowing the guys as I do so well, there’ll always be a soft spot here. I’ll always feel for those guys going forward because I know what they’ve been through, and how hard they work. I’m a cricket fan first and foremost.”
James Anderson believes England need to use home advantage better, claiming this year’s Ashes pitches have favoured Australia.
Anderson has been more observer than participant in the series, bowling just four overs on the first morning before a calf injury struck.
But as his country’s record wicket-taker, and the most prolific seam bowler in Test history with 575 scalps, his view carries considerable weight.
“We as a country – or cricket team, cricket board – don’t use home advantage enough,” he said.
“When you go to Australia, go to India, go to Sri Lanka, they prepare pitches that suit them. I feel like we could just be a little bit more biased towards our own team.
“We go to Australia and get pitches that suit them. They come over here and get pitches that suit them. It doesn’t seem quite right.
“I think they’ve probably suited Australia more than us.
“I would have liked to have seen a bit more grass but that’s the nature of the game here.
“When you’re selling out – like Lancashire selling out five days of Test cricket – it’s hard not to produce a flat deck but, you know, that’s one of the frustrations from a player’s point of view.”