The newborn boy is 10/1 to play in the Premier League like his father, but with far longer odds to turn out for either of his teams.
Klay is rated 50/1 with Ladbrokes to appear for Manchester United, 100/1 to play for Everton and the same odds to earn a senior England cap.
The bookmaker also offers odds on the Rooneys continuing the trend of baby names beginning with K, having also named their first son Kai.
Punters can get 5/4 on the third Rooney child following suit, or 4/6 on Wayne and Coleen opting for a name beginning with a different letter upon having another baby.
Any member of the Rooney family advertising Special K cereal is rated at 20/1, while the following names are all given long odds:
- Kourtney 25/1
- Karter 33/1
- Kassius 40/1
- Kris 40/1
- Khloe 50/1
- Kim 50/1
- Krystal 66/1
- Kristy 66/1
- Kanye 80/1
- Keith 100/1
- Kevin 100/1
- Kallum 100/1
More top news
Actor Harrison Ford had a near miss at a Californian airport after landing a plane on a taxiway.
The 18-month-old baby girl was in "excruciating pain" after suffering broken ribs, leg fractures and injuries to her spine, face and neck.
The "world's first transgender doll" has appeared at New York's Toy Fair and will go on sale in July.