The Magpies have been up for sale since February and, according to a recent statement from the club's chief executive Jason Turner, talks remain ongoing.
Local businessman Alan Hardy has so far been the only bidder to make his interest public, while a number of other parties from as far afield as the United States and China have allegedly been in the running.
Trew has told the Nottingham Post that he will return to his post of club chairman and concentrate on preparing them for next season in the bottom tier.
"I've set a deadline for the end of June for the club's sale," he said.
"While there are still interested parties, if a deal isn't concluded by then, I will take it off the market and we will push on."
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