The 21-year-old has missed the Railwaymen's last four league games after suffering limited cartilage damage on his knee, having made 17 appearances for the League One club this campaign.
Crewe manager Steve Davis is hopeful Mellor will be back in first-team action soon, but will wait for the results of the scan before confirming how much longer the defender will need to spend on the sidelines.
Davis told the club's official website: "Kelvin will undergo a scan and hopefully we will get some encouraging news on him.
"He has improved and the knee has settled down a bit.
"He took a bit of impact on it but he has worked hard and progressed well so we are hoping that he will be back with us again. The scan will inform us how much improvement he has made."