Jennings averaged just 18.11 in the five-Test series against India and, while Bayliss suggested his decent form on the tour to India a couple of years ago may count in his favour, he declined to confirm that it would be enough to ensure him another tour.
With Alastair Cook having retired, England are searching for at least one new top-order batsman and Bayliss confirmed that James Vince, Joe Denly and Rory Burns are all vying for a spot in the squad. Whether Jennings is retained will decide whether England have one or two spots available for them.
Ed Smith, the national selector, has previously expressed some confidence in Jennings despite the run of low scores. Pointing out that batting in the top order was treacherously tough during the India series, Smith noted Jennings' impressive "demeanour" and method and appeared to offer his tour hopes some encouragement.
In Jennings' favour is the fact he made a century on Test debut in Mumbai in December 2016 and followed it with an innings of 54 in Chennai. England expect to encounter similar spinning pitches in Sri Lanka. Those scores are, however, his only half-centuries in a 12-Test career and, in going 10 Tests in succession without passing fifty, he has set a grim new record for an England opening batsman.
"We have a selection meeting in a week's time and I am sure it will be discussed," Bayliss said. "I'm sure he will be a bit nervous about which way it will go. His history will be in his favour: he scored runs in India on spinning wickets.
"But he is a big boy and he knows runs on the board count as well. All of those points will have to be discussed and I can't say at this stage or another whether he will go or not."
If Jennings is not retained, it could mean a recall for Vince. Although he averages a modest 24.90 after 13 Tests, he averages 30.54 from the No. 3 position. As a result, Bayliss rated him England's "best No. 3" excluding Joe Root over the last few years. And, having gone back to county cricket and scored heavily in recent months - Vince is the second highest run-scorer in Division One this season behind Burns and is averaging 42.66 - Bayliss said he "had done what we asked of him since he was out of the team".
"If you take Joe out of the equation, Vince has probably been our best No. 3 over the last few years," Bayliss said. "I gave him the challenge when we dropped him to go back and score plenty of runs. Averaging 40 in county cricket is not good enough. You have got to average 50 or 60 and, take out this last game, he was close to that and made some big hundreds so he has done what we asked of him. Whether he makes the cut or not we will find out in a week."
While Bayliss admitted he had not seen much of Denly, he has had good reports from the team of scouts the England management now employ and confirmed he was being considered for a place in the squad.
"I have not seen him in the last couple of years," Bayliss said. "He has made some runs this year and apparently he is a decent player of spin. He can play the short ball but so can a few others. Vince for example. And obviously Burns is making a lot of runs at The Oval.
"I am sure all three guys will get a hearing and there might be more than one spot in the touring party."
Burns is, by a distance, the leading run-scorer in the Championship season. He is approaching the 1,200 run mark - nobody else has made 1,000 - and, while there is a suggestion he has made most of his runs on the flat Oval surfaces, three of his four centuries have come at New Road, Nottingham and Southampton. He also made 90 in Chelmsford and, at the time of writing, averages 95 away from home this season.
England expect to announce the limited-overs squad on Monday or Tuesday and the Test squad on the 23rd or 24th. Bayliss returns to Sydney for a brief holiday on Thursday, so will take part in the selection meeting via conference call.