The 18-year-old deputised for the injured Walcott and scored on his European debut for the Gunners as they defeated Olympiakos 2-1 in the Champions League at the Emirates Stadium on Wednesday.

And having followed an almost identical path in crossing from Southampton at a young age, Oxlade-Chamberlain is one to watch, believes Rice.

"From Arsenal supporters' point of view, they are going to be seeing a lot of this boy,'' Rice told Sky Sports.

"He has a big, big challenge to now get in front of Theo (Walcott). I know that Theo is a very strong-willed guy as well and he won't give in easy. It all bodes well for England anyway."

"Alex can go inside, he can go outside, he's got that injection of pace and I think what he needs now is to be consistent in his play. I am sure that is something he will be working on because he's certainly not a stupid boy."

"He has good people around him and they are telling him all the right things. Alex is very friendly with Theo and no doubt he will give him the benefit of his experience as well.''

Oxlade-Chamberlain was playing League One football for Southampton just last season but moved to the London side for a reported 12 million-pound figure.

He scored the opener in the Group F encounter, with Andre Santos adding another before David Fuster made for a nervy finish when he pegged a goal back for Olympiakos on 27 minutes.

Arsenal started strongly with two goals in the opening 20 minutes but looked shaky for the remainder of the match, particularly in defence.

"You can't turn around and say we had all of the game because that would be unfair,'' said Rice, standing in for the suspended Arsene Wenger.

"The first 20-25 minutes we were really in it well, but after that for about 15-20 minutes we maybe lost our way and they came back into it. From a defender's point of view, the goal was really poor."

Olympiakos boss Ernesto Valverde was left to rue his sides tardy start, with the visitors acquitting themselves well thereafter.

"When you have let in two goals so early ... that has affected us and left a bitter taste,'' he said.

"We were a bit disappointed because we tried to takes something out of the game. After we conceded the early goals, we performed quite well."

"However, when you face a team like Arsenal, you have to exploit all the opportunities you have to score, because they have the quality players to convert all their opportunities to goals.''