xDAI send from Metamask to Binance Exchange ETH deposit address

A few months back I had xDAIs into my Metamask wallet for participating in the IDO. Unfortunately, my address was not whitelisted and I wanted to convert the xDAI back to ETH (via DAI). However, due to caching issue the xDAI balance on the xDAI chain was showing as ETH balance instead of xDAI balance and by mistake I transferred them to my Binance Exchange ETH deposit address thinking they were ETH… Need to know if there is a possibility to recover these.

From what you are writing, these funds are currently in Binance address so only they can help you.