Thaksin's son Panthongtae Shinawatra on Thursday afternoon posted an image on Instagram showing his father tightly hugging a woman.
He said that someone sent him the photo while he was having his hair cut. He did not identify the woman.
Although the picture does not show her face, the woman's clothing matches the outfit Ms Yingluck was seen wearing when she left Suvarnabhumi airport for France.
Ms Yingluck and her son left Bangkok for Paris on Thai Airways International flight TG930, which departed at 12.05 am Thursday.
Speaking to reporters at the airport late on Wednesday, before departing Ms Yingluck asked for privacy.
"Let me take a leisure trip with my son. Please let's talk when I return in August," she said. Ms Yingluck is scheduled to return to Thailand on Aug 10. She said earlier she planned to visit France, the United Kingdom, Germany, Belgium and the United States.
Commentators have been speculating whether Ms Yingluck will return to fight her court cases, or go into fugitive self-exile like her elder brother.
A poll conducted by the National Institute of Development Administration (Nida) indicated that a narrow plurality of 41% to 39% believe Ms Yingluck will not return to the country by Aug 10, and most were certain she will attend her elder brother's 65th birthday party in France on Saturday.
There is also speculation that Ms Yingluck bought only a one-way ticket for her trip, but there has been no confirmation.
Social media also discussed the amount of baggage Ms Yingluck took with her. Some said she took 15 suitcases, while others said that was the total number of bags checked in for the whole group of 11 people travelling with her.