Coady has impressed in a back three with the Three Lions during recent international matches.
He could get another cap against Denmark on Wednesday in the Nations League, especially with Tottenham's Eric Dier a doubt.
Per the Express and Star, Southgate is also impressed with Coady's leadership skills.
He believes the player is valuable to have among the group, and that could cement his status as an England regular.
The 27-year-old even got a rare goal for the team in their win over Wolves at the start of this international break.
He was an unused substitute against Belgium in Sunday's 2-1 win.