Does the sentence “would you like to have dinner on me?” Make sense?

“On me” as in like I’ll pay for the dinner for both of us. I SWEAR I’ve heard this expression before when someone is gonna buy something for someone. Like “yeah its on me!”.

The reason why I was asking is because I was texting a girl and I said “Maybe we can have dinner on me afterwards?” But then I started overthinking when I reread the text and I feel like if I’m wrong about it being a saying or an expression that it could be taken as a sexual innuendo?

Or am I overthinking this?