The Reds fullback is off contract in June and a Bosman target for Real Madrid.
Redknapp wrote for The Sun: "Trent Alexander-Arnold has woken up and smelt the coffee — which is why I see him waving goodbye to Liverpool in the summer and signing for Real Madrid.
"If it were me and I fancied going out for a coffee or a cuppa after training, then I’d prefer to do so in Spain rather than Liverpool. Most would.
"No disrespect as it’s a great club and a lively city but there is just something magical about Madrid. So you can see the pull for a world-class right-back.
"It is probably Trent’s dream to play for Real Madrid and he’ll have seen pal Jude Bellingham do the same last year.
"Bellingham could have gone from Borussia Dortmund to any Premier League club he fancied but the magnetism of the Bernabeu is irresistible.
"My analogy about coffee seems trivial, of course, but there is so much involved in making a big move.
"Liverpool is a special club but you have to remember he cost them nothing, has given them years of service as a former academy player and now is the time to try a new adventure.
"Sometimes you can go stale and maybe it is time for him to go and play great football at another great club."