Misleading e-mails from people pretending to be from well-established retail companies are known to be circulating in the Glasgow area.
They indicate the recipient has placed an order with a company and ask them to click on a weblink.
But people have been warned that opportunists behind such scams may be trying to find out personal information, including personal and bank details, and shoppers have been warned not to fall into the trap.
Internet buyers are said to be particularly vulnerable to such scams in the run-up to Christmas because more carry out online transactions in the festive rush.
Glasgow City Council's Trading Standards team has urged anyone targeted by criminals operating online to contact them.
In one scam, a man from Kelvindale, in the city's West End, was contacted by someone purporting to be from online shopping company Amazon.
The e-mail, which was sent to a personal e-mail account, detailed an order number and asked him to click on a link to the company website.
But the man knew he had not placed an order with the company and the e-mail was reported to Trading Standards and Amazon.
Amazon said the e-mail was not legitimate.
A city council spokesman said: "The best course of action for any of these e-mail scams is to click 'delete' immediately.
"However, if anyone has handed over their details, or lost money, they should contact the Citizens Advice consumer helpline on 08454 040506 or their local Trading Standards Service."
A spokesman for Amazon said: "We would encourage anyone who thinks they may have received an e-mail from Amazon that is not genuine to contact us at email@example.com"
The company has issued the following advice to customers: "A 'phishing' or 'spoof' e-mail looks similar to a real e-mail from Amazon.
"It may direct you to a false website that looks similar to Amazon, which asks you to enter your account information and password. Your account information may then be used to commit fraud."
The company says it will never ask customers contacted by e-mail for bank details, card information, or their Amazon password.
Those who receive e-mails from companies are also asked to check the return e-mail address to make sure it carries the retailer's official name and not the name of another internet provider, such as msn or hotmail, as these accounts may be bogus.