Evans was surprisingly released by Chelsea, and has no shortage of suitors for his services.
Palmer believes that he is in pole position to snap up the young custodian, after first option Ola Tidman rejected the chance of a move to Edgeley Park.
"I am disappointed with Ola because I felt he owed me a bit of loyalty," said Palmer.
"But Rhys Evans is a good, young goalkeeper and fits the bill.
"He need to play first team football to further his career and it's no good for him to be stuck in the reserves at a Premiership club.
"I will be meeting with Rhys and his agent on Wednesday and hopefully we can sort out a deal."
