The 24-year-old was snubbed by Didier Deschamps for last week's friendly internationals, but Pochettino has claimed that he would invite the France boss to come to St Mary's Stadium to watch the midfielder in action.
"Until the final list is given he has his chances," the Southern Daily Echo quotes Pochettino as saying.
"I would actually invite the France national manager to come and see him direct as I think he has the skill and the quality to play with the France side and hopefully that will happen. I would be very pleased for him if that did happen."
Schneiderlin has been a Southampton player since 2008.