Bencherif, released by Notts County at the end of last season, has been training with the Spireites and has featured in their pre-season matches - most recently against Sheffield Wednesday at the weekend when the midfielder's performance drew praise from Cook.
The Blues boss appears keen on Bencherif but it was revealed at a fans' forum this week that Chesterfield's summer transfer activity, which includes the high-profile signings of Gary Roberts and Ian Evatt, has left the club around B£130,000 over budget.
Cook, who has signed 10 players during the close season, told Press Association Sport: "He's got certain qualities that we like but whether we can afford him or not remains to be seen. We're not silly enough to think we can just keep bringing players in.
"He's training so hard every day and he did well against Sheffield Wednesday on Saturday. He's working hard with fitness coach Shane Nicholson every day - he lost 2lbs in weight in one session last week. But we'll have to wait and see."
However, despite the Proact purse strings being stretched, Cook did insist the club's recruitment drive is not over.
He added: "No, it's not finished. It is ongoing every day and it never stops. We're looking for the best player for every position and we must be targeting the next one - the next Gary Roberts or the next Jack Lester.
"Where are they and how can we get them in? That's what we're always asking. Ian Evatt and Gary Roberts are here now but that's the culmination of months and months of hard work.
"I was after Gary Roberts the minute I walked into the club but sometimes your targets are not available and when they are available you don't think they are because you think you won't be able to get them. It has to be an ongoing process."
Meanwhile, Nottingham Forest midfielder David Morgan, who has been on trial along with Bencherif, has returned to the City Ground.