Friends of the former Spice Girl, who is rumoured to have begun dating Brand after they met at the London 2012 Olympics closing ceremony, reportedly told the Sunday Mirror that she cannot keep up with the comedian's "exhausting intelligence".
"Things are already cooling off," explained a source. "Russell's way into very intense spiritual readings that are just too much, even for Geri."
The singer was said to be "stunned" when Brand turned up at her home in Highgate, North London earlier this week. The comic allegedly brought along a DVD of Alan Bennett's series of dramatic monologues Talking Heads for the pair to watch.
"He is way too intense, full stop," the source continued. "He turned up with Talking Heads... it went straight over Geri's head.
"I don't think she really fancies him. She's just enjoying the attention. It will be yoga, sex and fizz, but it won't last the distance. He's off back to LA soon and she's not planning on going with him."
Other friends of the star have claimed that Halliwell has already got what she wanted out of the relationship, as it provided a distraction from her career worries.
The 40-year-old has reportedly recorded an album, but has struggled to land a new solo record a deal. Sources have also revealed that she was planning to launch a reality TV show, but the premise was rejected by both ITV2 and Sky.
"Geri hoped her performance with the Spice Girls at the Olympics would open doors but it hasn't," they said. "Russell's taken her mind off it all."