The Lebanese bank did not respond to a message seeking comment.
Bank statements seen by Reuters show how the Salameh accounts at AM Bank ballooned from $15 million in 1993 to more than $150 million by 2019.
Lebanese prosecutors suspect the accounts, from which regular cash withdrawals were made, were used to conceal money laundering activity, a Lebanese judicial source said on Saturday.
According to the lawyer, French prosecutors have summoned his client with a view of naming him a formal suspect.
If French prosecutors suspected Salameh of wrongdoing, they could not hear him as a witness, Sur said.