The Blues boss was reacting to a suggestion that his side needed to replace John Murphy who signed for League of Ireland club, St Patrick's Athletic, last week.
Benjamin had been on trial at Chester last month, but an eye injury forced him to pull out of the warm-up before City's friendly at home to Carlisle United and he returned home.
Davies said: "A big man up front would be advantageous and I have a couple of players in mind.
"If we receive a major injury to Kevin Ellison, Richie Partridge, or Ryan Lowe then I would need to bolster our attack, but I'm comfortable with those three players in our attack at the moment.
"At this moment in time a move for Trevor Benjamin is unlikely.
"The player needs to sort himself out with his eye problems and until he does then nothing will happen.
"I know Trevor is desperate to earn himself a contract after a trial period with us, but we're unable to do that right now."
Davies admitted he was keen to sign a goalkeeper to provide cover for John Danby before attempting to strengthen his attacking options.
The City boss wasn't happy with his club's 4-1 defeat at AFC Telford United on Saturday.
He added: "Our performance at Telford showed a few players where they are at which helps me before our first league game this weekend.
"We found out about our squad players which is part of the process of pre-season.
"I now know my starting eleven, but I hope the rest of our squad can bounce back from Saturday's setback."
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