A statement from Portsmouth yesterday revealed that the South Coast side had agreed a deal to sign the ex-England man and expected the signing to be confirmed when the star returned from holiday later this week.
However, it has emerged that Sheringham is believed to still be considering offers from elsewhere and does not yet have his mind made up about where he will be playing his football next year.
Speaking to the Daily Telegraph, Sheringham's agent Barry Nevill explained: "Teddy has agreed terms with Portsmouth but it is not a case of him flying back from holiday to sign for them later this week. There are still offers on the table from other clubs and Teddy will look at those first."
Whilst the European Cup winner has had offers from the likes of Charlton, Wolves, Millwall, Norwich and other clubs around the globe, the Royals are reported to be the only other club in serious contention for the 37-year-old's signature.
Royals Alan Pardew has publicly admitted an interest in signing Teddy, but appreciates that the lure of Premiership football could scupper his chances of completing such a signing.
Last week ran a story in our phenomenally successful 'Pardew's Piggy' series, looking at the likelihood of Sheringham becoming a Reading player. You can read that article here.