Liverpool's current first choice right back Alexander-Arnold has been heavily linked with signing for Los Blancos, with the Reds academy product in the final year of his contract.
However, it was his young deputy Bradley that will have stunned his suitors on Wednesday.
talkSPORT's commentator for the game, ex-England defender Pearce, said live from 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."
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As well as keeping former Reds target and World Cup winner Mbappe quiet, the 21-year-old's stats from the game speak volumes too.
The former Bolton loanee won more possession (9), more duels (8), more fouls (3), made the most tackles (4) and most assists (1) of any other player on the pitch.
No player in the Champions League has recorded higher figures across those categories in a match this season.
His crunching challenge on Mbappe quickly went viral on social media.
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Fans were in love with his performance, with one writing on X: "Conor Bradley came out here tonight and told Trent to go to Madrid."
Another wrote: "Mbappe has gone from living in Monaco, to living in Paris, to living in Madrid, and now Conor Bradley's pocket."
A third said: "Conor Bradley needs to calm it. Real Madrid will leave Anfield wanting to sign him."
Bradley went down with five minutes to go with the medical team coming on to attend to him.
Joe Gomez swiftly replaced him and the youngster received a warm reception from his manager Arne Slot.
Speaking to TNT Sports, Rio Ferdinand asked Slot about how impressed he has been by the club's young players this season, and how important they are to the squad.
To which he said: "They are. People always say, and I have to agree with them, that if you are coming through the academy, you know what it means for the fans, even more than the ones that come from different countries.
"It's special for the fans, but also for the club, that if they play on this stage against the reigning champions and they all do so well.
"We talk about Caoimhin [Kelleher], but also, you'll agree with me that Conor [Bradley] was really strong and Curtis [Jones] was really strong as well.
"It's nice for everyone to see, but it's not the way I pick my players or I select my team, they are cheap options as well which is also helpful with all these contract situations we have!"
Bradley has made 11 appearances for the club this season.
His time has been mostly restricted to coming off the bench, collecting 424 minutes of game time in total.
He has started both of Liverpool's Carabao Cup wins, the 3-2 win over Southampton last weekend and Wednesday's Champions League clash.
In total, Bradley has already made 39 appearances for the Reds, scoring once and grabbing seven assists.
He also lifted the Carabao Cup last term after his role from the quarter-finals onwards.
Just two years ago Bradley was playing on loan for Bolton, now he's starring in the Champions League.
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Alexander-Arnold, meanwhile, has won the Champions League and Premier League amongst other honours in his glittering Anfield career.
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He remained on the bench as Alexis Mac Allister and Cody Gakpo fired Liverpool to a 2-0 victory, while Mbappe and Mohamed Salah both missed penalties.
But should the Reds star leave for Madrid this summer, Bradley's showing on Wednesday suggests Slot has an excellent successor waiting in the wings.