Schneiderlin has been overlooked by France, despite impeccable Premier League displays for Saints.
Lallana said: "I am very surprised he has not been picked for France. Obviously, he is one of the best midfielders in the Premier League.
"He has every attribute going and I can't speak highly enough about him."
And Lallana points out: "Morgan has been here five years and can get a British passport to make him eligible for England.
"He likes the idea of playing for England. I room with him on away trips and it is something we have spoken about."
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