The Reds academy product, Virgil van Dijk and Mohamed Salah are all key players who could all leave Anfield come the conclusion of the season.
Salah spoke out about being 'more out than in' last weekend, while talkSPORT understands Van Dijk's future remains unresolved.
Alexander-Arnold, meanwhile, is being chased by Real Madrid and other European giants.
And out of the three, talkSPORT's Simon Jordan thinks the England international can be the one they can let go of.
"This is a good team, there's good players," he said on Matterface and Jordan on Thursday.
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"You don't want to lose Alexander-Arnold but also, is it going to be a catastrophe if you do?
"I don't think it is."
Asked by Sam Matterface whether he would indulge Alexander-Arnold and make him better paid than Van Dijk and Salah, the ex-Crystal Palace owner said: "No.
"With due respect to what these players are being paid and what the market wants to pay them, and if they can get something significant somewhere else, you either have to match it or find a mechanism that gives you the opportunity to keep the player.
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"If he wants to go, let him go. I don't think Trent Alexander-Arnold is as important economically because of the stage he's at in his career.
"If you're going to keep him until he's 30, the economics are going to go out the window anymore.
"So the only reason you put him on a longer term contract is you're protecting him for two reasons. One, you want to keep him in your camp, and B, you want to protect his economic value."
He continued: "I would suggest the most important two signings are Virgil van Dijk and Mo Salah. I think they'll do both of those."
Liverpool faced Los Blancos on Wednesday night in the Champions League, with the Reds winning 2-0 thanks to goals from Alexis Mac Allister and Cody Gakpo.
Arne Slot's side remain top of the Champions League as a result.
Alexander-Arnold was on the bench for the fixture, with his young deputy Conor Bradley - who could now be an injury concern - thriving in the clash where he bullied Kylian Mbappe.
talkSPORT's Stuart Pearce quipped Alexander-Arnold should ask for a contract with his suitors being present for the right back's performance.
Virgil van Dijk in awkward exchange with Spanish journalist over Liverpool future
He said at Anfield: "With Trent Alexander-Arnold sitting on the bench at the moment, he must be thinking to himself, I might just knock on the manager's door and say, please, have you got a contract for me?
"Because you've got someone who's been absolutely outstanding tonight, he's been brilliant.
"He's dealt with [Kylian] Mbappe, he's got forward, he's assisted goals, he's been everything."
The England defender has made 325 appearances for the Reds, scoring 19 goals and grabbing 83 assists.