cosy up to

verb2

1. •
   To come physically close to, using body language in an attempt to persuade another (often hesitant) party to snuggle or embrace.

   • He forgot the whole argument when she cosied up to him on the couch.
   • The kitten cosied up to the gruff old hound, and all resistance disappeared.
2. •
   To form a relationship with some one or some thing for the purpose of obtaining some benefit.

   • It is often suggested that politicians are too inclined to cosy up to big business in order to receive funds for election expenses.
   • The sales guys might be able to cosy up to the customers, but they are inexperienced in technical support.