The former Aston Villa defender likened the situation to the national cricket team, which features players such as South Africa-born Kevin Pietersen.
"We seem to have embraced the cricket team that has won the Ashes, but it is a really interesting, philosophical debate," Reuters quotes him as saying.
The issue was thrust under the spotlight after it emerged that Manchester United's Belgium-born Adnan Januzaj has been earmarked as a future England international.
"It's a difficult one. He's (Januzaj) not played for anyone else," Southgate added. I'm torn with it.
"The world is changing. People move and work abroad. It is important to know why someone wants to play for you."
FA chairman Greg Dyke has also weighed in on the debate, describing the idea of an England team limited to only English players as "extreme".