Kyle Walker started England’s first group stage victory over Croatia at right-back on Sunday, while Kieran Trippier played out of position as a left-back starting to the 1-0 win at Wembley.
Chelsea right-back James, 21, has not played since his club beat Premier League champions Manchester City to win the Champions League on May 29.
Manchester United left-back Shaw started the friendly 1-0 pre-tournament victory over Romania on June 6, but was an unused substitute against Croatia.
Chelsea’s Ben Chilwell – the other recognized left-back in Southgate’s Euros squad – has not been named to the 23-man squad for his first game of the tournament.
England will advance to the round of 16 with a victory over Scotland from Steve Clarke, who opened their campaign with a 2-0 loss to the Czech Republic on Friday.
Southgate: Maguire will be involved against Scotland
Meanwhile, Southgate has confirmed center-back Harry Maguire will be involved against Scotland.
The Manchester United defender has not played since he sprained his ankle against Aston Villa in the Premier League on May 9.