Sources have told ESPN FC that Robinson, who won 41 caps for England, is set to leave Blackburn Rovers when his contract expires next month after seven years at Ewood Park.
The 35-year-old made seven appearances for Blackburn this season, but found himself out of favour following the loan arrival of Jason Steele from Middlesbrough.
A source close to Robinson told ESPN FC: "Paul is very much looking forward to continuing his playing career and a new challenge."
A number of clubs at home and abroad are thought to be weighing up a move for the former Tottenham No.1, who has made over 300 appearances in the Premier League.
Leeds are among the sides monitoring Robinson as they look to build a side capable of mounting a serious push for promotion to the Premier League next season.
Robinson, who came through the ranks at Elland Road, played 95 times for Leeds before moving to Spurs and is thought to be keen on the idea on linking up with his former employers.
The move would likely be a welcome one among Leeds United's disgruntled supporters and go a little way to regaining owner Massimo Cellino's popularity at Elland Road.