Former France Under-21 international Amavi cost £7.7m when he joined Villa from Nice in July 2015 on a five-year deal.
The 23-year-old had looked set to move to Sevilla last month but that deal fell through.
Villa winger Leandro Bacuna is also on the verge of leaving the club, manager Steve Bruce confirmed on Wednesday.
Speaking to BBC WM 95.6 after his side's 2-1 EFL Cup win over Colchester, Bruce said: "We've agreed a fee with Marseille [for Amavi].
"There's a Championship club after Bacuna, that looks close to being over the line too."
Curacao international Bacuna, who can also play at right-back, has been with the club since 2013 and has scored eight goals in 129 appearances.
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Aston Villa left-back Jordan Amavi has signed for Marseille on loan with a view to a permanent move.