To have a sneaking notion for a lady, is to have a timid or concealed affection for her.
Well, I always used to have a sort of a sneakin' notion of Mary Stallins.--Maj. Jones's Courtship, p. 11.
An army such as me would fright the devil--
What are ye giggling at? Can't ye be civil?
There--that's well done; now I've a sneaking notion--
When I git hum--I'll git some grand promotion.--D. Humphreys, The Yankee in England, p. 102.