The France manager led Juventus back into Serie A following the hugely controversial Calciopoli scandal that relegated the club to the second division.
And now according to Italian publication Tuttosport, Deschamps is closing in on a sensational return to Turin as he wants to complete the work he left unfinished in 2007.
Tuttosport also report that Deschamps would be able to work under Juventus’ budget and he already has the club’s ‘blessing’.
This report comes just a day before current manager Allegri is set to meet club president Andrea Agnelli for talks over his future.
Allegri led The Old Lady to an eighth successive Serie A title this season but saw his side fail to take the next step in the Champions League as they were knocked out by Ajax in the quarter-finals.
Deschamps played 178 times for the Serie A giants between the years of 1994-99, winning three Serie A titles and a Champions League.
The 50-year-old could potentially be making the move to the Juventus Stadium following France’s historic World Cup triumph last summer.