updated 03/23/2014 AT 3:00 PM ET
•originally published 03/23/2014 AT 3:15 PM ET
Making it work?
She also attended several events earlier this year without her 9-carat engagement ring.
Although Hudson – who also has a son Ryder, 10, with ex-husband Chris Robinson of the Black Crowes – said in January that she wasn’t planning a wedding “anytime soon,” the source said she was working to save her relationship with the Muse rocker.
“Kate is not giving up,” the source told PEOPLE.
And so it seems!