The Spice Girl and funnyman have sparked rumours of a relationship after being spotted emerging from Halliwell's London home, as well as taking a guided tour of Hampton Court Place.
Halliwell and Brand apparently hit it off during rehearsals for the 2012 London Olympics Ceremony closing.
Band mate Melanie Chisholm has said that Halliwell has kept the status of her relationship with Brand a secret even from her fellow Spice Girls.
She told Magic FM: "I don't know what's going on. I know they get on really well. I'll have to quiz her on that one, the cheeky little minx!"
Halliwell has yet to publicly confirm her relationship with Brand.