Wearing a black baseball cap, Seann looked casual in a bold hooded top, jogging bottoms and trainers.
Stefania was equally as low-key in an orange sweatshirt and cropped leggings, while her hair was worn down and straight.
A source said: “Seann and Stefania regularly meet up for lunch and have been mates for a long time, but recently they have grown a lot closer.
“He was definitely keen to impress her and make her laugh, they seemed to have lots of flirty energy. When they said bye at the end it was a close and warm hug.”
They continued: ”Stefania has told pals she is still single, but she has a soft spot for Seann after all these years.”
The Sun said the pair have been close since December, when Stefania is reported to have taken Seann to the TRIC Awards Christmas lunch where they sat together.
However, a Strictly spokesperson told Express.co.uk: “It is the job of a Talent Executive to maintain relationships with contestants both past and present and any suggestion that this is anything other than a working relationship is complete nonsense.
“Strictly is a global brand that operates all year round.”
Last month, Stefania gushed about Seann as she posed arm-in-arm with him and another female.
She told her 5,117 Twitter followers: “Reunited with my favourite Funny man @seannwalsh Go see his tour it’s Brilliant http://www.seannwalsh.com xxx.”
Strictly’s production manger Theresa Hewlett and former professional Kristina Rihanoff were among those that liked the shot.
Seann and his long-term girlfriend Rebecca Humphries split shortly after he was filmed smooching Katya.
He and the Russian dancer, 29, apologised during an appearance on It Takes Two and went on to dance again on the programme.
She has since said her and husband Neil Jones – who also performs on Strictly – are “fine” after what happened.
“It was silly me. We all have moments. The reaction was really shocking but I tried not to look at the outside and just keep it together with us,” Katya said on ITV’s Lorraine recently.
Express.co.uk has contacted a representative for Seann Walsh asking for comment.