Justin Bieber and Selena Gomez are rumored to be working on a joint song about their relationship, rumors on Instagram and Twitter suggest.

"They are working on songs together but there is no timetable to release anything soon. They want it to be perfect, which is making things a little difficult because they only have one chance to release a song together for the first time," a source also told Hollywood Life. 

"Justin also considers it to be a big step in their relationship if he releases a song with her. So he is not really ready to show that commitment." 

Selena Gomez and Justin Bieber have been making headlines for their seemingly stable relationship-several of the "Birthday" lyrics singer's fans have been speculating over the possibility of the couple working on new songs.

She posted a picture on Instagram and Twitter of a video camera screen where she appears to be recorded-several fans commenting on the photo speculated whether it was a shoot for her popular "Birthday" track.

Selena Gomez also posted a photo on Instagram and Twitter of herself heading toward New York, where she regularly records her songs.

Last week she was spotted cuddling in a new picture with Justin Bieber on his Instagram page, confirming reports the couple is back together.

"Justin is getting really healthy, he wants to look good for Selena so he's working out a lot, they're both on a health kick," a source told Hollywood Life. 

"They're detoxing from all the partying and negativity right now. He's been hiking every day, that's his new favorite thing. And he's getting up early because he's not out partying all night, he's just been at home chilling with Selena."