Negotiations between the clubs over a fee are ongoing, with David Moyes looking to sign a player who will both provide centre-back cover and stands out as a prospect for the future.
Edwards was part of the England Under-19 side that won the European Championship last summer and represented the U20s at this year’s World Cup.
The 20-year-old was the subject of interest from both Chelsea and Crystal Palace last summer and was left out of Peterborough’s Carabao Cup win over Portsmouth last night.
Moyes has already signed Konstantinos Mavropanos to add to his centre-back options this summer, but both Kurt Zouma and Nayef Aguerd have been injury-prone while Thilo Kehrer is one of several players to have been linked with a move away before Friday’s deadline.
Depending on their other transfer activity, the Hammers may need to shift one foreign player in order to meet the Premier League’s squad requirements.
The Irons are pushing ahead with their bid to sign a striker, with talks over Corinthians striker Yuri Alberto ongoing in Brazil.
Personal terms are not expected to be an issue but the clubs are yet to agree a fee for the 22-year-old, who featured as a substitute in his side’s Copa Sudamerica meeting with Estudiantes overnight.
West Ham have also made another approach to PSG over a deal for Hugo Ekitike but are only expected to sign one striker this week and Eintracht Frankfurt remain favourites.