The talented goalkeeper and promising striker will spend time with Les Dogues with Ryan also set to trial with English League One club Sheffield United.
"Mat has a huge future ahead of him and we've had discussions with Sheffield United," Mariners owner Mike Charlesworth told SBS.
"It's down to Mat, and I will know when he gets back what his feelings are. But it's my understanding also that he is keen to go to Lille to trial along with Bernie Ibini."
Ryan, who is also being tracked by Danish club Randers and Scottish outfit Rangers, has previously spent time with Tottenham and West Bromwich Albion whilst Ibini trained with Belgian club Cercle Brugge on February.