Jennifer Aniston & Justin Theroux: Engagement Not 'Ringing' True

Jennifer Aniston, Justin Theroux Engagement Rumors
Jennifer Aniston and Justin Theroux at Los Angeles International Airport

updated 06/27/2012 AT 10:00 AM EDT

originally published 06/27/2012 AT 08:50 AM EDT

When Jennifer Aniston arrived at the Los Angeles International Airport after a romantic European getaway with Justin Theroux, buzz immediately built that she was sporting new bling on that finger.

So did she cap off her trip with an engagement?

Not quite ... Aniston, 43, prominently wears two rings: The diamond ring on her right hand is a ring that she's worn several times over the last year. The gold band that spells her name on her left ring finger is a ring she's also had since she started dating Theroux, 40, who has a matching one!

While photos of the couple, who began dating last May, at LAX set off a fresh round of engagement rumors, "it's the same ring she has worn forever on her right hand," a source tells PEOPLE.

Potential wedding bells aside, Aniston seems to be enjoying life with Theroux. Her happiness level is at "10-plus," she said earlier this year – before this trip which included yachting in the Mediterranean and stops in Paris and in Rome.

Reporting by JULIE JORDAN

Jennifer Aniston & Justin Theroux: Engagement Not 'Ringing' True| Couples, Jennifer Aniston, Justin Theroux

Aniston's name ring from different angles

Sipa; Everett; X17Online

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