The Gunners boss is likely to include the 18-year-old midfielders in the squad for the final Barclays Premier League game of the season at Sunderland on Sunday.
The duo have just returned from spells in the Coca-Cola Championship, Gibbs at Norwich and Randall with Burnley.
However, both players were only used sparingly - Gibbs making a total of seven appearances for the Canaries and Randall utilised more as a substitute, only gaining two starts.
"Now they need to show they are good enough," he said.
"They have, like everybody, to fight to play, and if they are good enough they play. It's as simple as that.
"They didn't play a lot and that's why it's sometimes disappointing you give them up to Championship teams and they don't play.
"(If) you want to play for Arsenal, you have at least to play in the Championship. When you go somewhere and you are on the bench, you cannot come back and say 'I have to play for Arsenal', because if you don't play in the Championship team it's difficult.
"For me it's very important to get them out and to see them play."
Wenger added: "For us it's part of education, to have a period of your life to play in a team who has responsibilities and to be under pressure and show how well you can do in the Championship.
"So it's just to get you used to realising that life is not as easy as it looks in the football world."
Wenger has plenty of English talent lower down the Arsenal ranks, and hopes they will soon all be in the first-team picture.