Allardyce could cultivate a whole new image for himself if he followed his instinct and broadened his horizons with a move to La Liga, says Martinez.
"People have a certain perception of Sam, but there is a forward-thinking side to him that would make him well suited to managing on the continent," said the Wigan boss, ahead of West Ham’s visit to the DW Stadium.
"That approach was very evident when he was in charge at Bolton, where he introduced sports science and other methods for bringing the best out of players.
"Maybe people don’t always expect that from him, but when you dig a little deeper, you see he has that side to him. He has incredible experience in the game, and he is very curious about all those different percentages that can help players perform at the very peak of their powers."