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Not only that, but plenty of other big names continue to be linked.
Here is the Liverpool.com verdict on the transfer gossip to emerge around the Reds today.
Alexander Isak (Newcastle)
Liverpool made contact about the possibility of signing Alexander Isak, although Newcastle has made it clear it doesn't want to sell, according to Fabrizio Romano.
It's claimed that the Reds made contact in April and earlier this month to understand the striker's situation.
His current club though is standing firm, with Arsenal also understanding that it probably won't be able to sign Isak this summer either — unless it does something "completely crazy" with its offer.
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No one is going to sign Isak this summer unless they're willing to offer an astronomical amount of money.
With the Magpies on course to qualify for next season's Champions League, their resolve will only grow stronger
The only ray of hope will perhaps come if they slip up against Everton on Sunday.
Rodrygo (Real Madrid)
Arsenal is now seriously considering a move for Real Madrid's Rodrygo, according to Florian Plettenberg.
Talks are said to have begun behind the scenes, with speculation over the Brazilian's potential departure growing recently.
That may come as a blow to Liverpool, with the Reds having been linked with Rodrygo a lot over the last year or so
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