Lavigne tweets her 'luv' for Jenner

"It really upsets me to read all the FALSE!! stories," Brody Jenner wrote about Avril Lavigne.

STORY HIGHLIGHTS

• Brody Jenner and Avril Lavigne haven't officially confirmed their split


• They took to the Twitterverse on Tuesday to declare their adoration for each other


• The couple's romance was first reported in May 2010

() -- Apparently there's no bad blood between and .

The exes, who haven't officially confirmed their split, took to the Twitterverse on Tuesday to declare their adoration for each other.

"It really upsets me to read all the FALSE!! stories," Jenner, 28, wrote. "Avril has always been there for me and is the closest person to my heart. I love her."

Lavigne, 27, wrote back, but unlike when they were a couple, she condensed the 'L' word to three letters instead of four.

"Luv u 2!!! @brodyjenner," she Tweeted.

The couple, whose romance was first reported in May 2010, could very well get back together, a source told PEOPLE after verifying the breakup.

Reps have not commented, and Lavigne will be touring Asia next month.

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