Orenuga has been released by Everton and been offered a chance of winning a deal by Carlisle boss Greg Abbott.
Abbott told the club's official website: "Femi was recommended to us and we are more than happy to invite him along so that we can have a look.
"Everton like him, but they obviously have the Premier League to think about, so he has been unfortunate in that they couldn't keep him on. He's had his injury but he has trained well with us [on Thursday].
"It's one where he was happy to come up to see us and we can have a look at him at close quarters before we decide what to do next."