Technically, it's probably like siblings, but it seems more like Mikasa has feelings for Eren that are unrequited. Or maybe Mikasa feels like she is Eren's servant?
Yes, Mikasa has romantic feelings for Eren. In Chapter 13,
Someone mistook Mikasa as Eren's girlfriend, to which she replies while blushing that 'they're family.'
In Chapter 50,
As Mikasa was thanking Eren, she was blushing and putting her face close to his face. They were in a hopeless situation, about to die. She might have seen this as an opportunity to express her feelings to Eren. When she put her face close to his, it looks like she was about to kiss him.
According to this, blushing can be caused by strong emotions. Seeing as how Eren saved her before and been there for her, it's no surprise that she would develop feelings for him.
Also, in Chapter 70,
look at Mikasa's face when Eren complimented Historia, who blushes and looks embarrassed. If that's not a look of jealousy, then I don't know what else it is.