England's Joe Denly during nets
Left-hander Jennings lost his place in the team after scoring 17 and 14 as England were beaten by 381 runs in the first test in Barbados, with captain Joe Root saying the 26-year-old would continue to work on developing his game.
"It gives Joe an opportunity," Root said. "It's disappointing for Keaton, he's done some excellent things and he will continue to... be a big part of this squad."
Kent right-hander Denly was part of England's squad for their last test series in Sri Lanka but never played.
Pace bowler Stuart Broad and left-arm spinner Jack Leach, who both sat out the first test, are also in contention having been named in Root's 12-man squad for the second test, which starts on Thursday.
England squad: Rory Burns, Joe Denly, Jonny Bairstow, Joe Root (captain), Jos Buttler, Ben Stokes, Moeen Ali, Ben Foakes, Sam Curran, Stuart Broad, Jimmy Anderson, Jack Leach.