Relevo says Ajax wants to sign the Swedish talent this summer.
Celta Vigo needs to sell some players to make room for new acquisitions for next season.
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Ajax are said to be ready to offer more than Celta Vigo paid for the midfielder, but under 10n.
Celta Vigo bought Swedberg from Hammarby IF in the summer of 2022 for 5m.
However, Ajax are not alone in the hunt for the U21 international. Many clubs around Europe are said to be monitoring Swedberg's situation in Spain.