"They have been quietly spending some time together. It is all very new and recent, and happened while he has been filming in New York," a source told the newspaper.
Gere, and Lowell, 52 parted are said to have parted ways after 11 years of marriage. The couple have a son, Homer.
Previously, Gere was married to Cindy Crawford.
Lakshmi, 43, was married to author Salman Rushdie for three years until they divorced in 2007. She then dated billionaire Teddy Forstmann until he died of brain cancer in 2011.
She also has a three-year-old daughter, Krishna Thea Lakshmi-Dell, with Adam Dell, the venture capitalist brother of computer maker Michael Dell.
Gere is currently in New York filming Time Out of Mind, in which he plays a homeless man trying to reconnect with his estranged daughter.