A team source told PTI that talks are at an advanced stage with Simons, who previously worked with the Delhi Daredevils in various roles including of a head coach, besides coaching in the Caribbean Premier League.
Simons worked with the Indian team for two years before being replaced in 2012.
The former South Africa all-rounder will bring a lot to the table at Pune, which is one of the two new teams to feature in the IPL beginning April 9.
The team will be captained by Mahendra Singh Dhoni and head coach will be Stephen Fleming, who was with the India captain at the now suspended Chennai Super Kings. Earlier in the week, Hrishikesh Kanitkar was named as the assistant coach of the Pune franchise.
"Life becomes slightly easy with him (Fleming) around. We know each other for long time," Dhoni had said on Monday.
"He is a fantastic coach. His management skills are very good. What I really like is that he is calm like me. It is good to have him and hopefully it will work for us."