England will select 15 players for the tournament on April 23 but International Cricket Council rules allow alterations to be made up to May 22 - wriggle room the selectors may use to parachute Archer in at the 11th hour.
The Barbados-born paceman, who has an English father and a British passport, completes a three-year qualification period later this month and will immediately come under consideration.
England are wary of upsetting the cohesion they have forged over the past few years but a 2-2 one-day series draw in the West Indies exposed limitations in the attack and strengthened Archer's hand.
Bayliss admitted discussions had taken place with and about the player in recent months, despite England's previous reluctance to talk publicly about the 23-year-old, and pointed to a May 3 date against Ireland and the subsequent one-day series against Pakistan as potential auditions.
"Jofra Archer's name keeps cropping up and I think at some stage we will give him an opportunity," said Bayliss.
"Those matches against Pakistan and Ireland, I think he will get an opportunity to show us what he can do. There was a little bit of contact made during the Australian summer, when there was talk about the date that he qualified, or how many days he needed to be back in the UK. He's said publicly that he's keen.
"There was certainly a discussion between selectors, coach and captain and that's been ongoing for a little while. Now we've got the opportunity to have a look at someone like that, why not take it?"
Archer has become a star asset on the Twenty20 franchise circuit but has limited 50-over experience, with only 14 List A games on his CV.
Bayliss has nevertheless been captivated by his versatility and can already see a number of roles he could fulfil.
"He's a bowler you don't get many of - someone who is able to bowl in all three phases of the game. He can take the new ball, he can bowl through the middle and he can bowl at the end, which is a good skill-set to have."
Good news for Archer would spell heartbreak for somebody else given England would need to publicly sacrifice one squad member to make room.
David Willey and Tom Curran are most vulnerable as the current second-string seamers, while all-rounder Joe Denly may be under threat if the squad is rebalanced.
"There is plenty of speculation all the time in the papers and I'm sure they read that," Bayliss said.
"They are on their Twitter and stuff, so they see it. If we do leave someone out of that initial squad I'm sure that will be explained pretty well to them.
"It is something we've got to think about and that will be one of the decisions we have to make. Firstly, is he (Archer) good enough to be in the team? And secondly, will that upset the apple cart to a degree that is affects the way we play?"
The final leg of a long Caribbean tour begins with the first of three Twenty20s in St Lucia on Tuesday.
Indian Premier League exports Ben Stokes, Jos Buttler and Moeen Ali have been excused from the series and Jason Roy will return home for the birth of his first child. New arrivals Dawid Malan, Sam Billings, Chris Jordan and Sam Curran fill the gaps.