Green’s Dictionary of Slang

1. besotted with, infatuated by, in love with.

1963		C. Rohan Down by the Dockside 212: She gave me a quid now and then. I never stood over her for it. She’s wrapped in me, see?
1969		A. Buzo Rooted I iii: I remember he was wrapped in a girl called Doreen once.
1979		Lette & Carey Puberty Blues 49: Kim told me that Bruce’s wrapped in ya.
1989		P. Munro Sl. U. 208: wrapped in love, infatuated, submissive, whipped.

2. fascinated by, enthused with.

[1785		Grose Classical Dict. of the Vulgar Tongue n.p.: To be wrapt up in any one: to have a good opinion of him, or to be under his influence].
1965		F.J. Hardy Yarns of Billy Borker 26: He was real wrapped up in Paris.
1969		A. Buzo Rooted I iii: You meet all sorts of super people. Richard took me to a turn and I was really wrapped.
1976		D. Ireland Glass Canoe (1982) 143: You were wrapped in this bloke, Shorty.
1989		R.G. Barrett Boys from Binjiwunyawunya 217: He wasn’t all that wrapped in Sydney, so he’d positively loathe Melbourne.
1992		K. Lette Llama Parlour 9: Oh why hadn’t I listened to my mates? [...] none of them were wrapped in me going Stateside.

3. delighted; overwhelmed with pleasure.

1976		Sydney Morning Herald 21 Jan. 1: $1,210 a week to play cricket ‘I’m just wrapped,’ Thomson said. ‘The offer is a fantastic one which never in my wildest dreams did I expect.’ [GAW4].
2000		Indep. on Sun. Culture 13 Feb. 1: I was wrapped [i.e. chuffed] to meet her.

4. see wrapped up