Saina joined the Bharatiya Janata Party (BJP) on Wednesday, saying she was inspired by Prime Minister Narendra Modi's policies and hard work.
After joining politics, Gambhir has since been elected an MP from Delhi, while Sandeep Singh won in Assembly elections in Haryana in 2019.
He is currently Sports Minister in Haryana.
It is now to be seen if Saina, who started her sporting career at the age of eight and was ranked world number 1 woman shuttler in 2015, will jump into the electoral fray.
Saina was born on March 17, 1990, to Harvir Singh Nehwal and Usha Rani in Hisar in Haryana.
After completing her initial schooling in Hisar, she shifted to Hyderabad after her father's transfer.
The family is settled there for long.
Saina's mother is confident that her daughter will make a mark in politics too, as she has done on the badminton court in the past.
Usha Rani said she was "very happy" over her daughter Saina's move.
"Saina was doing well in sports and she will do well in politics also.
The BJP is doing good. Saina is hardworking and will work hard in this field (politics) as well," she said.
Saina, 29, who promised to "contribute for the betterment of India", is the recipient of India's highest sporting award -- the Rajiv Gandhi Khel Ratna Award.
She was awarded the Padma Bhushan, India's third-highest civilian award, in 2016.
The shuttler, a former world number one, has won various international titles, including a bronze medal in the Olympics.