The striker has been deemed surplus to requirements at Stamford Bridge despite having a crucial role in Chelsea's strong finish to last season.
Ba struck against Liverpool in a crucial Premier League victory in April, having sent the London club into the UEFA Champions League semi-finals with a last-gasp goal against Paris Saint-Germain.
Diego Costa's arrival and the return of Romelu Lukaku have increased Jose Mourinho's attacking options and Ba is now set to move to Turkey.
Orman revealed the two clubs have completed negotiations for the 29-year-old's services and hopes to conclude the transfer as quickly as possible.
"Demba Ba is an excellent player," he told NTV Spor. "We have been in talks with Chelsea for a long time over bringing him to Istanbul.
"Talks are ongoing.
"Chelsea initially wanted £10 million for Ba but we have negotiated a price we are happy with.
"We'll tell the media once the final deal is done."
Ba would be the first major signing of the close-season for Besiktas, with only Ramon Motta added to Slaven Bilic's squad so far.
