Southgate has received praise for guiding England to the World Cup semi-finals, but the Three Lions manager also allowed Delph to temporarily leave Russia in order to attend the birth of his child.
The Manchester City man has reiterated his gratitude for Southgate, questioning whether many other coaches would have been willing to make such a gesture.
Delph is quoted by FIFA.com as saying: "He's one of the best people I've met in football. He's really a genuinely nice guy, very understanding and very caring but on the flip side of that he's very passionate too.
"I'll be forever grateful to him for what he's done for me like letting me go home for the birth of my third child, I am not sure many managers would have let that happen but he understands how important family is."
Delph is likely to feature when England face Belgium in the third-place playoff on Saturday.