PHOTO: AFP
However, coach Trevor Bayliss accepts it may take longer to convince him to give them up permanently if team management decide that's in the best interests of the side.
Bairstow was named in a 14-man England squad to face India at Southampton, while Hampshire captain James Vince returned as batting cover for the injured Yorkshireman.
Trial matches for new English '100' to be held in September
Even if Bairstow is passed fit to play, he is likely to do so as a specialist batsman only as England look to recover from a 203-run thrashing in Nottingham that cut their lead in the five-match series to 2-1.
England were fortunate that when Bairstow left the field injured at Trent Bridge they had a ready-made replacement on call in Buttler, England's wicket-keeper in limited-overs internationals but chosen as a specialist No 7 batsman when recalled to the Test side against Pakistan earlier this season.
Buttler had been a keeper early in his Test career and some observers believe that one way to bolster England's repeatedly fallible top order is to move Bairstow up a place to number four and have Buttler at seven.
Presently, England think it is asking too much of Bairstow, who is proud of the work he has done to improve his keeping, to bat higher than five and be behind the stumps, especially if England are in the field for a long stretch at the start of a Test.
Equally, if Buttler — whose 106 at Trent Bridge was his maiden Test century — performs well with the gloves, it may be he remains as England's red-ball keeper.
"It's like any injury, if someone comes in and does well, then you have a decision to make," said Bayliss.
But the Australian admitted: "That'll be the hard thing, trying to convince Jonny. If that was the way we went, it would certainly be a deep conversation with someone like that. Jonny's a reasonable bloke. If that's the way we wanted to go...in the long run, he wants to play Test cricket."
Root urges beaten England to follow Buttler and Stokes's lead
England deploy Bairstow as a specialist batsman in the limited-overs formats and would be prepared to do so in Test cricket.
"He is a world-class batter, we know that," said Bayliss. "I think he has improved his wicket-keeping over the last couple of years. Jos will have to do some hard work as well. He's been keeping a lot in one-day cricket — but keeping 100 overs-a-day can be difficult, day after day, Test after Test."
A longer-term problem for England remains a lacklustre top order which has seen them slump to 100 for four or worse in half of their last 62 Test innings.
England were all but beaten in the third Test when they lost all 10 first-innings wickets in a session to be bowled out for a meagre 161.
That latest collapsed prompted Bayliss and England captain Joe Root to convene an unscheduled team meeting.
"It is not the first time it has happened and we speak about it every time," insisted Bayliss, a former coach of Sri Lanka coach. "The guys we have in the team play in a certain way."
Buttler and Ben Stokes showed the top order how it should be done with a fifth-wicket stand of 169 in the second innings.
"We know they have got to play the situation and the conditions, like those two guys did," said Bayliss. "They are all aware of what they need to improve. It's just taking a little while longer than they would like and we would like. I'd love to be able to give them a magic pill and it happens overnight."
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