Singer Cheryl announced the arrival of her first child by posting an image on Instagram showing One Direction's Liam holding their newborn.
Bookmakers say Alfie is a popular choice as Cheryl has spoken of her liking of the name in past interviews.
Simon is another frontrunner, according to William Hill and Coral, due to the couple's friend and colleague X Factor boss Simon Cowell.
Coral has priced Simon as the favourite in the betting stakes with 10-1 odds, while Liam and Will have been placed at 12-1.
David Stevens, of Coral, said: "Now that Cheryl and Liam have welcomed a baby boy, we've launched betting on the name of the pop star couple's little one and Simon has emerged as the favourite"
William Hill cites Alfie as the top choice with odds of 4-1, with Simon in fourth place at 14-1.
The bookmaker's other top names are Harry at 10-1 and Rickie at 12-1.