The U21 trio were called up to the senior side and may well get their debuts after five players made their England bow during the 0-0 draw against Germany on Friday.
"Those (three) guys have fitted in off the field which helps them to fit in on the field," said Southgate.
"They are good players so in training they look fine."
Southgate also confirmed that Eric Dier will retain the captaincy for the friendly at Wembley, while Joe Hart will replace Jordan Pickford in goal.
On the same day as England's goalless draw with the world champions, Solanke, Cook and Gunn all played in the U21's 2-0 victory over Ukraine.
"Angus has worked with the under-21s with us (Southgate's coaching team) and he is playing in the league," said Southgate. "The other two are captain of the Under-20 World Cup winners (Cook) and the Golden Boot winner in the Under-20s World Cup (Solanke).
"They have got good pedigree and we won't hesitate to put them on the pitch."
When asked about his thoughts on selection ahead of the World Cup in Russia next summer, Southgate added: "I am open-minded.
"I have a list and if I had to pick the squad tomorrow I know who it would be but that can change in six months because of form and players emerging.
"We watch the players very closely with their clubs and have succession plans to who is second, third and fourth choice. That is constantly updated."