Wicket-keeper Bairstow injured the middle finger on his left hand fielding a James Anderson delivery during England's Third Test defeat at Trent Bridge last week as India reduced the home side's lead in the series to 2-1.
"When you see that a batsman has a weakness and he feels uncomfortable in some way, you'd prefer to work on that aspect," said Shami.
"It's not just me - any fast bowler will want to target his weak zone - so we will definitely look at that."
However, Bairstow remains keen not only to potentially play as a specialist batsman, but also keep hold of the gloves instead of handing over responsibility behind the stumps to Jos Buttler.
"The swelling has gone down," he said on Tuesday. "I'm going to try and keep wicket in training this afternoon as well."
England have a ready-made replacement in Buttler, who took over from Bairstow after the Yorkshireman was injured in the 203-run defeat in Nottingham.
"You obviously want to play, so If I'm not able to keep wicket then I would like to think I'll be a specialist batsman," added Bairstow.
"But at the same time I'm desperate to try and keep my place as the wicket-keeper.
"I'm very, very keen to keep my spot as the wicket-keeper -- because I would like to think it's gone pretty well over the last 38/39 Test matches that I've been keeping for England."
The fourth Test of the five-match series begins on Thursday.
First Published: August 28, 2018, 9:52 PM IST