Stoddart has been sidelined for the best part of a year after suffering a horrific double fracture of his leg in Wales' World Cup warm-up match at Twickenham last August.
The 27-year-old, who has scored five tries in eight appearances for Wales, has returned to light training with Scarlets conditioning coach Brad Harrington and the region are cautiously optimistic of having him back for the beginning of the RaboDirect PRO12.
"The X-rays have come back fine and Morgan is currently back running and doing some light rugby sessions," a Scarlets spokesperson told the South Wales Evening Post.
"We are hoping he will be ready to play a part in pre-season and then for the start of the league season, but obviously it was a serious injury and at the moment we have to be mindful of that.
"He is having a specific training programme with Brad Harrington to get him up to speed.
"Morgan is an integral member of our squad and hopefully we can see him back in action very soon."
Stoddart isn't the only Welsh international to be on the comeback trail at Parc y Scarlets. Rob McCusker has undergone shoulder surgery and continues his rehabilitation.
Gareth Maule is also recovering from an ankle operation, while Aled Davies is poised to return in the Scarlets' pre-season matches following knee surgery.