Gill injured his left thumb while fielding and is a major doubt for the match, the Times of India and other media outlets reported, citing sources. The team did not provide immediate comment when contacted by Reuters about Gill's condition.
India's Rishabh Pant will be fit to keep wicket in the second Test against New Zealand after an injury scare, confirmed coach Gautam Gambhir on Wednesday.
India captain Shubman Gill led his team to what he described as a "crucial" 23-run win in the third T20 international against Zimbabwe at the Harare Sports Club on Wednesday.
India's top stars have been rested for the series starting July 6 and the 15-member squad has only two players including Yashasvi Jaiswal and Sanju Samson from the ongoing T20 World Cup team.
Shubman Gill and Sai Sudharsan both hit centuries in a record-equalling 210-run opening stand that helped Gujarat Titans defeat Chennai Super Kings by 35 runs in the Indian Premier League in Ahmedabad on Friday.
Centuries from skipper Rohit Sharma and Shubman Gill helped India entrench their control of the final Test against England with a 255-run lead on Friday.
India's skipper Rohit Sharma celebrated the Test series win over England by saying his team's young players had filled the shoes of missing veterans to shine in cricket's toughest format.
Shubman Gill and Dhruv Jurel guided India to a series-clinching five-wicket win over England on day four of the fourth Test on Monday.
Shubman Gill (18) and Ravindra Jadeja (three) will resume after the lunch break hoping to get the remaining 74 runs.
Opener Gill, playing his second match of the series, featured in three 50-plus partnerships to help India, who lead the series 2-1, reach 289-3 at stumps.
Opener Shubman Gill blasted a blistering hundred as India routed New Zealand by 168 runs in the third T20 International to secure a 2-1 series victory on Wednesday.
India's Shubman Gill dedicated his maiden international hundred to his father after getting "schooled" by him for missing the mark earlier, the top order batsman said after his match-winning 130 in the third one-dayer against Zimbabwe in Harare.
Shubman Gill made his first international hundred as India beat Zimbabwe by 13 runs after a tense finish in Harare on Monday to complete a 3-0 ODI whitewash.