The London Evening Standard says the Holland international has overcome an ACL injury in his first season with the Gunners to become a first-choice for manager Mikel Arteta.
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Timber's current deal runs to 2028, but Arsenal now intend to extend that further and up his terms.
Arteta said recently, "I think he's a really good example of another one that hopefully is going to have a long career with us.
"I rate him a lot. When you're talking about a total player, he has almost every quality that you want from a defender."
