1
general::
Contrive a secret plot or scheme, especially with selfish motives. For example, I think he has designs on my job, or Mary has designs on her sister's boyfriend. This term uses design in the sense of "a crafty plan," a usage dating from about 1700.
American Heritage Idioms
2
general::
Phrase(s): have designs on someone or something
Fig. to have plans to exploit or somehow take advantage of someone or something. • Mrs. Brown has designs on my apple tree. I think she’s going to cut off the part that hangs over her fence. • Mary has designs on Bill. I think she’ll try to date him.
McGrawhill's American Idioms And Phrasal Verbs