Ads have appeared on websites including Craigslist offering the tests for around $20 (£12.80).
One ad reads: ‘I have positive pregnancy test for those of you who need a little help holding onto your man through the holidays, shoot me a message for $20 each.’
Fake positive pregnancy tests have been available for some time, and are advertised on sites like eBay as a ‘prank’ gift.
Another Craigslist post, which has since been removed, asks: ‘Wanna lock your man down just in time for Christmas?’
But police have warned how buying these tests in a bid to tie down a partner could be classed as blackmail.
Gary Mason, of Kansas force in the US, said: "For example, if a married man is having an affair and he tried to break it off with the girl, and she became upset and decided to present this fake pregnancy test and demand money, otherwise she would tell the spouse. That would be a level of blackmail."