The Premier League side have reportedly made a €40 million bid for the 20-year-old centre-back, but Ajax technical director Marc Overmars confirmed the club have offered him a new contract in response.
However, the Colombia international, who was named their Player of the Year last season, was not in the matchday squad for the game against Heracles in Almelo.
Coach Marcel Keizer confirmed his absence is due to the uncertainty over his future.
"Marc Overmars and I have both had contact with Davinson about everything surrounding him," he said before the game.
"Of course, I hope he stays at Ajax, but tonight we play without him. Only with players 100% focused on the game."
He scored seven goals in 47 games in all competitions for the Eredivisie side, but has been revered for his excellent defensive work.
Ajax signed Sanchez for €5m from Deportivo Cali last summer and tied him to a five-year contract.
He arrived in Amsterdam just weeks after winning the Copa Libertadores with the Colombian side, playing every minute of the competition.