The midfielder has trained with the Stags this summer following his release by Notts County at the end of last season.
However, there will be no deal for the 25-year-old at Field Mill and Cox will instead explore other options.
"He's not with us now. We've had to move on," Cox said in the Nottingham Post.
"I've got players champing at the bit and some good, young players coming through and we want to look at different avenues."
Bencherif started his career at Nottingham Forest before moving on to Macclesfield Town in 2009 and then County two years later.