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It would have made more sense for them to move for a new signing after convincing Salah to sign a short-term contract. They are taking a very risky step with this move. Liverpool will finish this season as champions but next season they might not be in the same comfort zone. I don't think they planned very well, but with better planning they could have dominated the league for a few more seasons...
Liverpool must move quickly to find a replacement for Mo Salah who has not yet extended his contract. They need to bring in a quality player as Mo Salah successor because the position is very central and requires balance to maintain the sharpness of his mini attacks. Rodrygo is still young, he also has the quality to enter Liverpool main line up.
Real Madrid must view Liverpool's interest in Rodrygo as a threat and Ancelotti must pay more attention to prevent the player from turning his attention to other clubs. If he gets guarantees in Ancelotti first team squad, maybe he will stay.