Green is a free agent after two years with the Stags which have seen him score 56 goals - 25 of which came last season as he helped fire the Nottinghamshire club to the Blue Square Bet Premier title and promotion back to the Football League after a five-year absence.
The 26-year-old has attracted a lot of interest from other clubs this summer and has had a trial at Championship side Birmingham, but Cox still hopes to have Green at his disposal for the 2013/14 campaign.
"He is ambitious and I'm not going to have a go at someone for that," the Stags boss told the club's official website.
"I spoke to him recently and I'd love him to sign a new deal here, everyone knows that.
"We have a good relationship and I would like to think that if the big boys decide not to offer him anything, he would want to come back here and play for us."
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