'My number one choice is Simon because I like the name,’ he revealed in an interview with TV presenter Terri Seymour.
The 54 year-old dad-to-be also said his second name choice would be ‘Eric’ – after his father, who passed away in 1999.
'His birthday is going to be very close to my dad’s birthday’ said the music mogul, adding that his father would be proud and amazed if he were here.
It is not known whether his girlfriend Lauren Silverman has had any say in the name choices.
Simon also gave an insight into what kind of father he might be, saying he wants his son’s upbringing to be ‘relaxed.’
'Be cool about it,’ he said, ‘and don’t worry about things to much… the way my brother and I were brought up, it was kind of relaxed. There were no self-help books.'
Keen for his heir to take on the Cowell empire, Simon said he wants ‘ to teach him how to do my job as quickly as possible.’
‘I really would like the idea of teaching him how to run the business,’ he added.
It has recently been reported that the X Factor judge – who will welcome his mini-me into the world in February 2014 – plans the marry the mother of his child.
'Simon and Lauren have spoken very openly about marriage and he’s told pals he may even propose by the end of the year,' a source revealed to Heat magazine.