The Dutch giants want £50m but the Gunners are believed to be confident a compromise can be reached.
Personal terms are understood to have been agreed with the 15-cap Netherlands ace.
Timber, 22, can play right or centre-back and has two years left on his Ajax deal.
He was heavily linked with a move to Manchester United last summer.
And Red Devils fans were convinced a deal would be struck due to Timber’s past relationship with Erik ten Hag – who he worked under at Ajax.
But the switch failed to be completed as Lisandro Martinez and Antony proved to be the only two players from Ten Hag’s former squad to arrive at Old Trafford.
Timber signed a contract extension back in August to keep him at the Dutch giants until 2025.
However, in March he dropped a big hint he could be on the move.
As quoted by Ajax Life, Timber said: “Transfer? You never know what crosses your path.
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“This summer I will look at my options and make a decision.
“I feel good at Ajax, that’s important for now. Last summer there was interest, but I chose to stay at Ajax.”
And Man Utd supporters were given renewed hope Timber will be signing for them when he was spotted at the FA Cup final earlier this month.
But Arsenal will be confident they can hijack a deal for the Dutchman as they bid to bolster their squad following their return to the Champions League.
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