The defender will become a free agent when his Newcastle United contract expires at the end of the month.
Simpson – who joined the club, initially on loan, four years ago from Manchester United – lost his Newcastle place to January arrival Mathieu Debuchy.
Long-running talks over a new deal for Simpson at St James’s Park broke down last year, and the 26-year-old is keen to stay in the Premier League.
The Salford-born player will assess his options next week after returning from a holiday in the United States.
Simpson is also interesting newly-promoted Cardiff City, but it remains to be seen whether the club will table an offer.
West Bromwich Albion have also been linked with a move for Simpson, who came close to joining Wigan Athletic in the January transfer window.
Simpson made 138 appearances for United.
Source: Newcastle United Mad