The 21-year-old has scored six goals in 28 league appearances for Toulouse this season from the right-back position, while his performances for Ivory Coast have also impressed, with some tipping the youngster to shine at the World Cup finals in Brazil this summer.
According to reports in France Football, Chelsea scouts watched Aurier in action during Saturday night's match between Toulouse and Lille. However, Arsenal are also firmly in the hunt to sign the former Lens full-back.
The Gunners are poised to lose current first-choice right-back Bacary Sagna in the summer, when the France international's contract expires, and have identified Aurier as a potential long-term replacement as doubts over Carl Jenkinson persist.
Chelsea already have the reliable Branislav Ivanovic as their first-choice right-back, while Cesar Azpilicueta - a right-sided full-back by trade - has taken the place of Ashley Cole in the Blues' starting line-up this season.
But Jose Mourinho might be tempted to make a move for Aurier if his scouts report back with positive feedback after running the rule over him.
It's believed that a bid of around £6m would be enough for Arsenal or Chelsea to force Toulouse into selling their prized asset - but, if the youngster continues to progress at his current rate, that fee will look a bargain in a few seasons time.