"I would like to play two spinners somewhere in this tour and currently he's thought of as one of the top two spinners in the country."
England's bowling was substandard at Lord's, where Australia strolled to a 405-run win, but their top order is a much bigger concern.
England have slumped to 52-3 or worse in eight of their past 13 innings, with Adam Lyth, Gary Ballance and Ian Bell all under pressure to retain their spots.
"I'm sure all of the players know. It wouldn't be a surprise to any player in the team that when you play badly, positions are going to be looked at and discussed," Bayliss said.
"I'm sure it certainly will be.
"It's a concern that we are 3-40 or 4-40 and they know that.
"Sometimes they're almost trying too hard."
Bayliss conceded he had limited information about those players pressing for selection.
"I'll be relying pretty much on the others. [Jonny] Bairstow, obviously I know of, and a few of the guys in the one-day team," he said.
Bairstow has scored a century in his past three county games, which suggests he is at the front of the queue.
There's been plenty of talk about the test pitches in England, but Bayliss pointed out the county wickets might be the bigger issue.
"There's always a lot of low scores in first-class cricket here. Is that preparing our batters to actually bat for a long time? Possibly not."
- AAP