London-born Rice has three senior caps for the Republic, but they all came in friendly matches meaning the 19-year-old could yet represent England.
Gomez had been tipped as an outside chance to make England's squad for the World Cup in Russian Federation but ultimately missed out due to injury.
Southgate has remained loyal to the majority of his World Cup squad.
We're going to be playing Spain who have to replace David Silva and [Andres] Iniesta, and the questions are: is it Koke, [Cesc] Fabregas, Saul or Thiago Alcantara?
'It's been more enjoyable than 20 years ago, when I was nearly as famous, ' said Southgate, jokingly referring to his penalty miss at Euro 96.
The Three Lions open their UEFA Nations League campaign by taking on Spain at Wembley Stadium connected by EE on Saturday 8 September, before hosting Switzerland in Leicester three days later for a Kick It Out worldwide.
Gareth Southgate has selected a 23-man squad for England's September fixtures.
"I want us to try to capture what we had this summer", said Southgate.
But Shaw appears to be benefiting from a more conciliatory approach from Mourinho in recent months, putting in the kind of energetic displays United was expecting when it made Shaw the world's most expensive teenage player by signing him for $46 million in 2014. For me a proper football player is player of consistency.
The 23-year-old has not played for his country since a 1-0 defeat to Germany in 2017 but has returned at the expense of Old Trafford team-mate Ashley Young in the Three Lions' first squad since the World Cup.
"You see a lot of things in the media that go on about what our dressing room is like, but we have a really good spirit, a really good group of lads who want to work and achieve big things here". He is a good young player.