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
Sky has withdrawn its recommendation for the £11.7 billion Fox deal following Comcast’s £22 billion offer.
Three Court of Appeal judges are analysing the latest stage of a life-support treatment dispute.
Ms Markle joined Harry and William at services in London to honour the fallen.