After the final whistle Conte went over to Messi and was seen talking to the Barcelona star for a while as they walked off the pitch arm in arm.
Messi had earlier produced a masterclass to stun Chelsea, scoring after just two minutes, before setting up Ousmane Dembele for the second and then adding the third.
Conte on what he said to Messi at FT: When you have the opportunity to make a great compliment to Messi, it’s right to recognise a super, super, super top player. I’m very pleased to have the opportunity to give him my compliment.— Samuel Marsden (@samuelmarsden) March 14, 2018
Conte asked if he'd like to coach Messi one day: "I think Leo wants to stay until the end of his career with Barcelona. We’re talking about an impossible situation." #cfc— Liam Twomey (@liam_twomey) March 14, 2018
Conte’s future at Chelsea remains the subject of speculation with many reports claiming he may quit the Premier League side at the end of the season.
The Blues also face a battle to qualify for next seaon’s tournament, they are currently fifth in the table, four points off a Champions League spot with eight games left to play.