The 29-year-old Stimpson has won five consecutive Zurich Premiership titles – one with Newcastle and four with Leicester – but with Leicester yet to secure a Heineken Cup place for next season, reports in France state that he could be the next one in an influx of foreign players.
Leicester team-mate Perry Freshwater has already signed on the dotted line with Perpignan, as has Australian centre Daniel Herbert and Irish lock Mick O'Driscoll.
Stimpson has 19 England caps to date, having toured with the Lions to South Africa in 1997, but he has struggled to pin down a regular place in the England side down the years due to the form of fullbacks such as Jason Robinson, Matt Perry and latterly Josh Lewsey.
Should he sign for the Catalans, he would continue a growing trend of foreign players moving to French shores, where there are no salary cap restrictions, as in England.