The former England goalkeeper believes that if Wilshere can prove his fitness, Gareth Southgate should include the midfielder in the squad for the tournament in Czech Republic.
Wilshere has not played for the Gunners since ankle surgery in November and a subsequent "minor procedure" in February.
Seaman told talkSPORT: "I'd like to see him go (to the European Championship).
"He has not played a lot of football this season and, if he is fit, he should go."
Seaman's comments come after increasing publicity over whether Tottenham's Harry Kane should join up with U21s.
Gary Lineker said it would be a "national disgrace" if clubs pulled their players out of England duty.