All-rounder Ben Stokes got injured on third morning of first Test against Sri Lanka. PHOTO: AFP
The hosts are due to announce on Thursday their squad for the first of a four-Test series at Lord's starting on July 14.
Buttler lost his Test place to fellow wicket-keeper Jonny Bairstow in November while there are doubts over all-rounder Stokes's fitness to bowl as he recovers from knee surgery following an injury suffered while playing for England against Sri Lanka in May.
Stokes's worth as a batsman was underlined by his stunning 258 in a Test against South Africa in Cape Town in January while Buttler looked in good touch when making runs during England's recent 3-0 one-day series win over Sri Lanka, wrapped up in Cardiff on Saturday.
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Buttler has not played red-ball cricket this year but Australian Bayliss said after England's 122-run win in Cardiff: "He could play as a bat, I'm sure... he wouldn't have any problems at all. I think he could handle it.
"He's certainly in contention, that's for sure."
As for Stokes, Bayliss said: "He's playing the next four-day game (for Durham) as a batsman and might bowl some short spells, depending on how he's gone in the last few days in the nets.
"He's a guy who has made plenty of runs in Test cricket already -- he has to be discussed, I'm sure."
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England will have to make at least one change to their top order following number three Nick Compton's decision to take time out from cricket following a run of low scores in the 2-0 Test series win at home to Sri Lanka.
"Long term, I think Joe Root is our number three," said Bayliss.
"Rooty would have to want to do it -- it's a big change, and he's done well at number four.
"But my way of thinking is you put your best batter at number three."
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James Anderson, England's all-time leading Test wicket-taker, is struggling with a stress fracture of the shoulder blade in his right, bowling arm.
"There will be an ongoing assessment between now and the Test, giving him every chance to make himself available," said Bayliss.
England have one fixture before the Pakistan series begins, a lone T20I against Sri Lanka at Southampton on Tuesday.
Sussex paceman Tymal Mills, reputed to be the quickest English bowler now playing, could make his international debut there.
"I'd love to see him play. I won't be the sole selector, but from my point of view, it would be great to see someone like that charge and give it everything," said Bayliss.
"It's good to see some batsmen ducking and weaving."
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