The 28-year-old midfielder spent five months on loan at Meadow Lane after being told by the Hatters that he had no future at the Blue Square Bet Premier club.
Boucaud made 23 appearances for the Magpies, the last of which came in the 2-1 defeat to MK Dons on New Year's Day, and manager Keith Curle has made no secret of the fact he would like to sign the player.
A statement on the club's official website said: "Notts County Football Club is currently in transfer negotiations with Luton Town and Andre Boucaud with the hope of bringing the player to Meadow Lane on a permanent basis.
"The Kenilworth Road club has requested a fee for the midfielder.
"First-team manager Keith Curle would like to keep hold of Boucaud, but until a deal can be struck he will remain a Hatters player."