The Ibrox side will be without a number of players due to injury when they host Motherwell on Sunday including Kieran Dowell, Todd Cantwell, Nico Raskin and Danilo, and Beale expects to utilise the full depth of his squad over the coming week.
And he revealed that 16-year-old Rice – a former Motherwell academy player – could feature at some point.
He said: “Having the four injuries to Kieran, Todd, Nico and Danilo means there’s some quality missing. But we still had 20 outfield players available in training for the Betis game.
“And I trust a couple of the young ones to make a step up this season. It’s just about when – not if – they make that step up. If you play for this club you want to be playing 60 games a season because that means you’re doing well.
“This is why we build a squad and hopefully – and it’s one game at a time – but by the end of this little batch we’re praising the squad and the strength of it.
“We know we have Ryan Jack and I’m telling you we have a heck of a player with Bailey Rice. He’s 16, not 17 until next month, so when I introduce him to this mad house will be important – and we’ll have to protect him – but I’m telling you he’s ready."
Rice made his senior Rangers debut last season as a late substitute in a 3-0 win at Livingston. It remains his only senior appearance to date although he also featured for the first-team during pre-season friendlies this summer.
“He’s a player with a lot of potential,” Beale added. “He’s trained with us now for a long, long time and through pre-season."
The Rangers manager has also warned of the challenge facing his side as Motherwell look to extend their long undefeated run away from home.
The Fir Park side have not been beaten on their travels in the league since Stuart Kettlewell became manager in February and have lost only once this season, at home to St Mirren last weekend.
Rangers are similarly buoyant after winning their opening Europa League group match against Real Betis on Thursday night but Beale recognised there was no scope for resting on their laurels with three big domestic games coming up at home this week.
The Rangers manager said: “It will be a completely different challenge obviously. Motherwell have got a fantastic away record. I’m told they haven’t lost in a long, long time.
“So, it’s an interesting game at the weekend. They’ve had a week to prepare and a chance to have a look at us.
“It’s important that we don’t have too many pats on the back. It’s important that we dust ourselves down and recover well.
“We’re right in the thick of the action now. We’ve got six games in around 20 or 21 days. When you win, you want the next game to come around quickly. Luckily for us they do this week.”