Carsley led England Under-21s as they won the European Championship in 2023 for the first time in 39 years.
Gareth Southgate resigned as England manager two days after defeat by Spain in the 2024 Euros final last month.
The path from under-21s manager to caretaker boss of the senior team is well trodden, with Howard Wilkinson, Stuart Pearce and Southgate all stepping up after taking charge of the Young Lions.
Southgate went on to secure the job permanently and led the side for eight years, reaching a World Cup semi-final in 2018, a World Cup quarter-final in 2022 and Euros finals in 2021 and 2024.
The Football Association has been conducting a search for a replacement and a job advert was published on their website.
The FA has not commented on the search for Southgate’s replacement but has always made clear it has had an “interim solution in place”.
Carsley, 50, is a former Premier League midfielder who played for clubs including Derby and Everton in a 17-year career.
He moved into management and took charge of Coventry, Brentford and Birmingham on a caretaker basis before joining the England set-up in 2020.