Bayliss names his squad on Saturday morning for the series opener at Lord's while contending with a number of injury concerns in his bowling attack, Jimmy Anderson and Stuart Broad among them.
And the chief cause of anxiety in the batting line-up is the collapse in form endured by opener Haseeb Hameed, who has failed to reach a half century since returning from a successful winter in India.
Bayliss, however, welcomes the number of options available as England prepare to open hostilities against South Africa next Thursday.
“In the two years I've been here it will be the toughest selection meeting that I've had. It's a good problem to have when you're struggling to know which guys to put in,” Bayliss said.
“It will depend what happens at the top and where we decide to bat Jonny Bairstow. There are a few possibilities.
“Someone like Mark Stoneman has been doing well at the level below. Does Joe Root go back to three and we put an extra middle order player in?
“Where does Jonny Bairstow bat? This is all up for discussion and we'll come up with an answer.”
Broad is struggling with a bruised left heel but it is hoped the Nottinghamshire all rounder will be able to play in Saturday's One Day Cup final at Lord's as a warm-up for the first Test.
“We'll know more tonight (Thursday) before our selection meeting in the morning,” Bayliss said.
“He's been training the last couple of days when we've been putting him through more of a test and if he comes through that he'll play in the one-day final as a test for the Test match.”
While Hameed is struggling, England can take comfort in the rampant form of Alastair Cook, who has struck three centuries since relinquishing the captaincy to Joe Root.
“It's great that after giving away the captaincy he's still got that hunger for runs and it was great to see him making another hundred yesterday (Wednesday),” Bayliss said.
“I'm sure he's looking forward to this Test series. I'm sure that as an ex-England captain it will be bit of a juggling act for him in terms of how much he gets involved.
“I know that he and Joe Root get on really well. Cook is very well respected in the team and I'm sure if he feels something needs to be said, he will.”
England must also decide whether to give Gary Ballance another chance at Test cricket on the strength of his fine form for Yorkshire this season.
“It's great to see him scoring runs and I'm sure he'll be spoken about at the selection meeting quite heavily,” Bayliss said.
“The one thing that Gary has always had in his favour is that he is mentally tough.
“That's the reason why he is able to come back from being dropped a couple of times and why he's been able to score a lot of runs for Yorkshire this year.
“There's no reason why someone like that can't come back and a make a success of international cricket.
“At some point the selection panel will have to make a decision on whether it's time to look at someone new. I'm sure that will be a discussion point.”
