The 20-year-old has reportedly attracted interest from several Premier League clubs after breaking into the Leicester team this season.
Southgate has named Moore in his squad for the forthcoming European Under-21 Championship qualifiers against Finland and San Marino.
"I've watched him a couple of times myself and we've also had good reports from our scouts," Southgate told TheFA.com.
"Leicester have been doing well and he's a good defender, he's athletic and he seems to enjoy defending, which is an art - although I am bound to say that as an ex-defender.
"But I think he's played well for a consistent period and we think it will be good to get him into the squad and see how he compares to the others. It will be good for him to come in and train with some of our guys and see how he develops."
Moore has made 17 appearances for Leicester this season in all competitions.