Sagna has been forced to watch from the sidelines with a broken leg as Jenkinson has enjoyed an ever-present run in the Premier League for Arsenal so far this term.
The French international admitted that he has been impressed with the young defender's rapid development as his replacement.
He told the club's official website: "He has been really good, and has learned a lot. He is a bit more confident with the ball, and is very solid as a defender.
"He brings a lot to the team, and I am very happy for him because he is a hard worker, a very good guy and is going to be one of the best."