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The Liverpool defender was overlooked for upcoming World Cup qualifiers against San Marino, Albania and Poland, with right-backs Reece James, Kyle Walker and Kieran Trippier all getting the nod.
Explaining his decision, Southgate said: "I don't think he's played at the level he's been at during the last few years."
Alexander-Arnold's omission irked fans on social media and former Liverpool and England captain Gerrard has said he disagreed with Southgate's call.
Offering to give the 22-year-old andy advice, he labelled Alexander-Arnold "world-class" and "the best right-back the country has got".
"One thing's for sure, I'll always be there for Trent," Gerrard told the Athletic . "
"It goes without saying, any second of the day. I wouldn't make the first move. He's a man himself. He knows where he's at.
"Gareth Southgate makes the decisions there. I don't necessarily agree with that decision. But I'm not the England manager. I think Trent is the best English right-back in the country.
"One thing I've learned from being a player is you can't always be 10 out of 10. When you do come off, you need that support, love and attention from your manager more than anyone else. So, I was surprised by the decision but that's my opinion and my opinion is not important in this.
"Trent is a world-class right-back, he's the best right-back the country has got. We've got other fantastic right-backs by the way. But in terms of the loaded side of the question, I'm there for Trent and any of the other Liverpool players at any moment of the day."
Alexander-Arnold's levels have dipped this season and coincided with reigning champions sinking to seventh in the league after a dismal run of form.
Having given him time off in anticipation of a call-up, Jurgen Klopp is said to have been surprised by Alexander-Arnold being axed.
The Athletic say Southgate phoned the Liverpool youth product and told him he is very much in contention for a recall going into the European Championships.
Former Reds and England striker Peter Crouch feels Alexander-Arnold has to go to the Euros despite not being selected in the most recent squad.
"The selection, or should that be 'no-selection', that surprised me most of all involved Trent Alexander-Arnold," Crouch said in his column for the Daily Mail.
"I like James, he's had an outstanding season but if Trent doesn't go to the tournament it will remind me of the time Sven Goran Eriksson overlooked Jermain Defoe for Theo Walcott in 2006.
"Trent is a top player and surely you have to find a place for him in the squad?"
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