The Serie A side announced they had sacked Andreazzoli on Wednesday (AEDT), two days after a 5-1 thrashing at the hands of Parma left it 19th in the table.
"In the next few hours, news on the make-up of the technical staff will be announced and a presentation news conference will be held for the media," he club said.
Motta is expected to be named as Andreazzoli's replacement in what would be his first head coach job since he retired from playing in 2018.
The former Italy international has been coaching the Paris Saint-Germain Under-19s side since ending his playing career with the Ligue 1 champion.
Motta won league titles and the Champions League with Barcelona and Inter before heading to PSG in 2012, where he won 18 trophies in six years.
He spent the 2008-2009 season with Genoa, helping them to qualify for the Europa League.
The 37-year-old was quoted by Tuttomercatoweb as saying he is "ready to get going."
Genoa, which won only one of its first eight Serie A games of the season, hosts Brescia on Sunday (AEDT) before travelling to champion Juventus on 31 October.