Wrap is used after these nouns:
gift

firmly, securely, tightly
loosely
carefully, neatly
individually
Each apple was individually wrapped in paper.

up

around, round (esp. BrE)
He wrapped his arms tightly around her waist.

in
She wrapped the child carefully in a blanket.

warm, warmly, well
Make sure you wrap up warmly if you're going out.

against
We went outside, well wrapped up against the cold.

in
Christine was wrapped up in one of the blankets.

Wrap is used with these nouns as the object:
bandage, cloak, gift, leg, package, parcel, present, shawl, sheet, towel