England suffered a heavy 336-run defeat to India in the Edgbaston Test, resulting in the five-match ICC World Test Championship series being levelled at 1-1.
Archer, who joined the England squad at Edgbaston last week, hasn't played Test cricket in more than four years, but recently made a red-ball return at first class level for Sussex.
"You could keep trying to build his overs up and play him later in the series, but it could be too late by then. I think he will play. He's played one game for Sussex, he was around the team at Edgbaston and bowled a bit. I just feel like you've got to play him. It's too crucial a game not to," Anderson was quoted by ICC.
England coach Brendon McCullum, however, stopped short of guaranteeing the return of Archer, but did say the towering right-armer was fit and available for selection.
"Jofra is looking fit, he's looking strong, he's looking ready to go, and he'll come into calculations. It's hugely exciting. He's buzzing as well. He's obviously been through his injuries and his time out of Test cricket.
"We all know what he's capable of achieving in Test cricket and we hope that when the opportunity does arrive for him, he's able to recapture and also improve on what he's been able to do already in that form of the game,' McCullum said.
"Jofra is looking fit, he's looking strong, he's looking ready to go, and he'll come into calculations. It's hugely exciting. He's buzzing as well. He's obviously been through his injuries and his time out of Test cricket.
Also Read: LIVE Cricket ScoreEngland squad for third Test: Ben Stokes (c), Jofra Archer, Gus Atkinson, Shoaib Bashir, Jacob Bethell, Harry Brook, Brydon Carse, Sam Cook, Zak Crawley, Ben Duckett, Jamie Overton, Ollie Pope, Joe Root, Jamie Smith, Josh Tongue, Chris Woakes.
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