According to a report from Tuttosport, should Fabio Paratici join the club as sporting director, he will seek a reunion with the 55-year-old.
Paratici reportedly held talks with AC Milan last week and is regarded as the front runner to take over the vacant position.
The Italian is understood to have already made plans for the 2025-26 season, which start with the appointment of Conte.
Conceicao replaced fellow Portuguese manager Paulo Fonseca in December, but has failed to turn the club’s fortunes around.
Milan are in serious danger of missing out on a place in next season’s Champions League, sitting down in ninth with 47 points from their 29 games.