Make a move on somebody
Definition 1 of 2
Pro Tip 1/3Subtle Approach
Often implies a cautious or indirect way of showing interest to avoid rejection. 
He tried to make a move on her by liking all of her social media posts.
Pro Tip 2/3Colloquial Use
The phrase is casual and might be inappropriate in formal contexts. 
At the networking event, he didn't feel it was right to make a move on a colleague.
Pro Tip 3/3Risk of Misunderstanding
Using the phrase can be misinterpreted as objectifying or disrespectful. 
When he said he wanted to make a move on her, his friends warned him to be respectful.