Spice Girl Halliwell, 40, who has already released two yoga DVDs, finds a spiritual connect with Brand, reported Sun online.
"Geri has said they have a spiritual connection through yoga and they practice 'asana' together," a source said.
"Russell is actually very good at just sitting still in silence. It is something that has acted as a bond for him and Geri as their relationship blossoms," the source added.
The two got to know each other during the London Olympics closing ceremony.