updated 01/17/2012 AT 7:50 AM ET
•originally published 01/17/2012 AT 3:45 PM ET
The couple have indeed split, a source tells PEOPLE. But the source says the lovebirds, who were inseparable for much of their romance, could very well get back together.
Jenner hasn t commented on the breakup rumors directly, but seemed to address it with a cryptic post on Twitter saying, “Everybody RELAX.
Meanwhile, Lavigne is focusing on her work and is headed out of town. The singer wrote on Twitter Tuesday, “Getting excited for my shows in Asia next month. Japan, China, Philippines, Malaysia C U SOON!”
The unlikely duo started getting cozy in the middle of 2010. At the time, they took a trip to Vegas together and posted flirtatious Tweets about “love.”
Jenner, 28, a former Hills regular was previously linked to fellow reality costars Kristin Cavallari, Lauren Conrad and Jayde Nicole. Lavigne, 27, filed for divorce from ex-hubby Deryck Whibley in Oct. 2009.
A rep for Jenner did not return requests for comment on the split.