Heidi spent nearly a decade as part of the Sugababes after replacing Siobhan in 2001 following the release of the band’s first album.
While Heidi has not been part of their recent comeback, the group have said she is still “a massive part” of their history.
Addressing Heidi’s absence in an interview with The Sun, Keisha said: “I think collectively we would all agree that Heidi had her part of it and is a massive part of Sugababes. For her to have done that journey with us, she is just as important to the journey of Sugababes.
“We’ve seen Heidi and there’s no bad blood or anything like that.”
Mutya added: “There’s no time to have bad blood with people. You’ve always got to give people their flowers.”
During their pop heyday, Sugababes became known for their ever-changing line-up.
After Heidi replaced Siobhan in 2001, Mutya quit the band four years later and was replaced by Amelle Berrabah.
The only remaining founding member Keisha was then replaced by Jade Ewan in 2009, with the final line-up releasing their last single Wear My Kiss in 2010.
The original line up reformed under the name Mutya Keisha Siobhan – often shortened to MKS – in 2013 and released single Flatline, but a full comeback was beset by delays.
In 2019, MKS regained the right to record as the Sugababes, and released a cover of Sweet Female Attitude’s Flowers with DJ Spoony.
Earlier this month, Sugababes announced a nationwide tour for the autumn, and have suggested they will finally release the material they have recorded together.
Keisha told The Sun: “Writing and trying to be creative, it takes time – although we say that and when we get in the studio it is quick.
“But the point is, we are trying to get everything together. We’re only just coming out of Covid and stuff, so we’re hopeful.”