Questions over Wenger's future have resurfaced in the wake of his side's 5-1 defeat to Bayern Munich on Wednesday night, with a seventh consecutive last-16 exit from the Champions League now looking guaranteed.
Wenger's current deal with the Gunners runs out at the end of this season, and Dixon is beginning to believe that it will spell the end of the Frenchman's 21-year stay at the club.
"He just seems so low. I think he's realising that with this team he's getting no response from them. They're not doing themselves justice or him," he told ITV Sport.
"That is the first time where I've seen him where I've thought, 'he thinks it's time'. The fact that he hasn't been able to get a response from the players in the last few weeks might be the final straw."
Arsenal will look to bounce back from the humiliating defeat when they take on non-league side Sutton United in the FA Cup on Monday.