But the 26-year-old midfielder opted instead to join the Hammers, signing a three-year contract picking up a lower seven-figure signing on fee.
Not even the potential prospect of Champions League football – if Fenerbahce beat Benfica in a two-legged qualifier – could persuade Wilshere to pick them over the club he supported as a boy.
Wilshere revealed earlier this month it had been an “easy decision” to leave Arsenal for the Hammers on a free transfer.
Pellegrini said: “He’s a very important player, not just because of his experience but his quality. He’s come from a winning club, he used to play Champions League and that mentality now comes to West Ham and we need to use it.”