Cook, who admits to questioning his role as captain following last winter's Ashes whitewash, is preparing to lead England in a one-day international against Scotland in Aberdeen on Friday.
According to the BBC, Cook said that although he gave consideration to the future after a grueling winter, however, he was dissuaded by Broad and his other teammates, who urged him to carry on as captain.
Cook, who also lead the ODI side to a 4-1 reverse in the series that followed the Ashes in Australia, has however, started the domestic season in good form by scoring two centuries for Essex in the County Championship and he said that he would have been wrong if he had not questioned his role as a leader after the winter they had.
But Cook expressed his gratitude to his teammates, the England and Wales Cricket Board (ECB) and managing director Paul Downton for their support, adding that although it is a great honour to captain England, he needs to justify that honour and support by winning games of cricket.
Following England's single ODI against Scotland, they will play a five-match series against Sri Lanka, the report added.