Ryan McKee, 25, is alleged to have "engaged in sexual activity" with the girls, who were 14 and 15 at the time.
Mr McKee, from Kinning Park in Glasgow, represented Scotland at the Commonwealth Games in Delhi in 2010.
He faces a total of six charges relating to a five-year period from March 2010 to August 2015. Mr McKee denies the charges.
He is due to stand trial at Glasgow Sheriff Court in August.
Court papers claim that in each of the charges he was "in the course of his employment as a gymnastics coach".
It is alleged he repeatedly kissed each of the girls.
In one of the charges, Mr McKee is accused of "coercing an older child" into looking at a sexual image and of "communicating indecently" with her by sending her naked pictures of him and requesting that she send him naked pictures of herself.
He is also charged with asking another girl to send a picture of her chest and asking the third girl if she wanted him to send her "sexual images" and asking for her to send the same to him.
A former international gymnast has been charged with sexual offences against three teenage girls.