Mary-Kate Olsen and her lover Olivier Sarkozy have found a novel way to spend time together.

The pair have only been dating a short time and have been seen going out for dinner and to basketball games together.

But Us Weekly reports that the duo went training at a private gym in New York City's West Village recently and was very cosy together.

"They were both smiling a lot and very cute with each other," a source told the publication.

They warmed up side-by-side on elliptical machines and Mary-Kate was seen taking "a sip from a giant SmartWater, then offered him a swig."

"They lifted kettle bells in the air and looked in the mirror," the source added. "He jumped in place while looking at her."

"At one point, they rested and he stepped close to her and sweetly gave her 10' with his palms."

Mary-Kate, 26, and Olivier, 42, appear to be head over heels despite their 16-year age difference.

"MK is constantly complaining about boys not being mature enough for her. She got the kids out of her system," another insider recently told the publication. "Now being a businesswoman dominates her time, and she is rarely impressed with guys."