Blanc, it should be remembered, was sacked from Al Ittihad, the reigning champions of Saudi Arabia, after the 0-2 defeat against Al Nassr on Friday, and at that moment Conceição's name came up among the main targets, as Flashscore reported.
Now, according to Fabrizio Romano, Conceição has "opened the door" to an agreement with Al Ittihad, although talks are ongoing, with the aim of having the Portuguese coach in Saudi Arabia immediately.
As well as Conceição, Luciano Spalletti and Xavi have also been tipped to succeed Laurent Blanc.
Al Ittihad are currently third in the Saudi Arabian Super League with nine points from four games.
In the AFC Champions League, they lost their first game 2-1 to Al-Wahda and are aiming to qualify for the knockout stage, which means finishing among the top eight teams in their group.