The 26-year-old is thought to be surplus to requirements at St James’ Park, following the arrival of Mathieu Debuchy from Lille, and could be allowed to leave this January.
West Ham are rumoured to be leading the race for his signature, with manager Sam Allardyce being a long-term admirer of the ex-Manchester United man.
However, he may face competition from Fulham, who are keen to strengthen their defensive options, and QPR, who are looking to spend in order to avoid relegation.
A potential stumbling block could be Simpson’s current injury status. The full-back suffered a broken toe in the Magpies’ 7-3 defeat against Arsenal, and is not expected to return to first-team action until late January at the earliest.
Simpson was consistent performer under Alan Pardew last term as Newcastle secured qualification for the Europa League.
But, the club are believed to be willing to allow him to leave after an underwhelming start to the new campaign.