The Reds fullback has faced a backlash over the past week after news broke that he is ready to commit to a move to Real Madrid this summer.
Ferdinand said on his personal Rio Ferdinand presents podcast: “You should be saying thank you and good luck. Trent Alexander-Arnold, you didn't pay a penny for him. He came through your academy, he’s one of your own and he won it all.
“This kid has been there, worn the shirt, been one of your best players, most productive players in one of the most successful periods in recent years.
“And because he's choosing to go and leave the club, not for a rival, not for a team in the Premier League, he's going to the biggest club right now in the world, which is Real Madrid. You should be saying: ‘You know what, I'd love him to stay but well done’.
“You should be clapping him off and giving him a hero's welcome when he eventually comes back in 15 years, when he finishes his career. The club have to take some responsibility. They've allowed him to get to this point.
“When he was 18 months out, he should have told the club that he wanted to leave... rubbish. There are too many moving parts in this. He might not have known then where he wanted to go.
“If it was Real Madrid he wanted to go to only, 18 months ago they have got a right-back who's one of the best in the world. (Dani) Carvajal was flying, captain of his country, winning the Champions League, so the spot's not there for him.
“The situation might have been sped up because of Carvajal's injury. So the situation changes. They're not taking none of that into account. I just feel it's not all on Trent Alexander-Arnold.”