The former Sheffield United defender, 19, has earned an extended trial at Gresty Road after impressing in the Alex's pre-season friendly games against Wolves and Birmingham.
"Max has done well since he came here. I am pleased he has stayed with us and given us more time to make our minds up about him," Thordarson told the club's official website.
"He is a good young player who wants to do well in the game. Our decision as to whether to offer him a contract or not will depend on the budget and what is available to us.
"If we can afford to do something then I would make it happen."
Source: Team_Talk