If someone is interested in purchasing an item you have listed on eBay, they need to complete the transaction via eBay.
If you receive a message asking you to remove the listing from eBay and instead just email a PayPal invoice to their personal email account (basically, asking you to sell it outside of eBay so you can save a few bucks on fees), it may sound tempting but it is against eBay rules.
You can learn more about the policy and guidelines here.
When a message is opened via the eBay messaging system, you will see a red flag and the following reminder from eBay:
“Do not respond to the sender if this message requests that you complete the transaction outside of eBay. This type of offer is against eBay policy, may be fraudulent, and is not covered by buyer protection programs.”
Perhaps the potential buyer doesn’t realize it or they do not care, but the best thing you can do as a seller is report it here. While it may sound tempting to make some extra money by not paying the outrageous eBay fees, it is NOT worth losing your eBay account and reputation! Be smart and honest.