
Edwards has been in a relationship with Liverpool FC footballer Alex Oxlade-Chamberlain since early 2017.
After the announcement, bookmakers Betfair gave odds on their choice of name, with Eleanor (5/2) and Henry (5/2) as favourites for the girl and boy options.
Little Mix band members are represented - Jessica is 9/1, Jade 14/1 and Leanne (spelled traditionally) 20/1.
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All four of the baby's grandparents' names are there, with Alexander (Perrie's father) short at 15/2. The others - Wendy (33/1), Mark (33/1) and Deborah (50/1) are longer priced.
Jurgen, after Oxlade-Chamberlain's manager at Liverpool is a rank outsider at 100/1 - while a nod to his Sunderland-born skipper Jordan Henderson is 16/1.
Betfair spokesman Sam Rosbottom said: "Little Mix fans were overjoyed to see Perrie Edwards follow her band-mate Leigh-Anne Pinnock in announcing her pregnancy.
"Ellie is the name of Perrie's best friend at a 5/2 that is the favourite girls' name - while Henry, also at 5/2 is a nod to Arsenal fan Oxlade-Chamberlain's hero growing up, Thierry Henry.
"We back the couple to go somewhat more traditional with their choice - however, Perrie's Little Mix bandmates are all represented in the girls' list, the favourite of the three past and present members being Jessica at 9/1."
Perrie is the second member of the girl group to announce a pregnancy this month.
Earlier in May, Leigh-Anne Pinnock revealed she is expecting a baby with footballer fiance Andre Gray.
The odds in full:
Girl
Eleanor – 9/2
Amelia – 7/1
Isla – 9/4
Jessica – 9/1
Lily – 15/2
Mia – 11/4
Jade – 14/1
Leanne – 20/1
Wendy – 33/1
Deborah – 50/1
Boy
Henry – 5/2
Alexander – 15/2
Noah – 11/4
Benjamin – 7/2
Louis – 8/1
Jordan – 16/1
Teddy – 20/1
Patrick – 25/1
Mark – 33/1
Jurgen – 100/1