The teenagers have already featured in the Premier League this season and were also part of the Asia Tour 2013.
Gnabry and Akpom have been named in the squad for the third-round clash at the Hawthorns and Jenkinson believes the duo have bright futures ahead of them.
It's a cup that of course we have a good chance of winning and I'm really looking forward to it. I've got great memories personally of playing in itCarl Jenkinson
“If I had to pick a couple [of exciting youngsters] I'd probably say Serge Gnabry, who the Arsenal fans have seen quite a bit of so far,” Jenkinson told Arsenal Player.
“I'd say Chuba Akpom [too], who has been involved with us quite a lot lately. He's been on the bench and he made his league debut against Sunderland. He's a strong, physical presence and he can finish as well. I'm sure you will see him.”
Arsène Wenger has included six players under the age of 20 in his squad for the third-round game and Jenkinson is ready to step up and help the younger players if needed.
“I suppose if we're going on previous seasons, maybe the boss will put out a younger side,” he said.
“I guess I will be one of the more experienced players, which for a 21-year-old will be nice. I remember I was in a fairly similar position last year when we played Reading. I think I had played pretty much every Premier League and Champions League game up until that point so I felt like one of the more established players at that stage.
“It's a cup that of course we have a good chance of winning and I'm really looking forward to it. I've got great memories personally of playing in it, notably the game last season against Reading.”