sliniti

1. to drool; to slobber
   Beba stalno slini jer joj izlaze zubi. — The baby keeps drooling because she's teething.
2. colloq. (za/nad + noun) to drool over
   Svi momci sline za njom. — All the guys are drooling over her.
   Slinio je nad novim telefonom u izlogu. — He was drooling over the new phone in the shop window.
3. (of the nose, a cold) to have a runny nose
   Dete je prehlađeno i stalno slini. — The child has a cold and his nose keeps running.

Figuratively it takes za or nad + instrumental (za njom); the colloquial sliniti se means "to make out sloppily".