The 21-year-old joined from Crystal Palace in the summer and has enjoyed an impressive first season at St Mary's to date.
Clyne shone during Saturday's 3-1 defeat of Liverpool and now links up with England's Under-21 squad to face Romania and Austria.
Asked if the full-back has the ability to make it into Roy Hodgson's senior side, Saints boss Pochettino said: "Yes, I think he has the characteristics and the skill to one day play in the England national team if he keeps on growing in the way he is growing now.
"We are talking about possibilities for the future. We can't really know what will happen to him in the future. I think we need to be really patient with young players.
"Sometimes getting too much praise weakens a player. It is important that they build their career up and to keep learning and growing as players by not placing great expectations on their backs because I think that can be counteractive to them."