Italics are for emphasis and certain types of titles. They attract attention but not as much for scanning; italics are to be used for emphasis within a sentence. If you want to draw attention to text for scanning, make the text bold or change the color and it stands out outside the current paragraphs.
Italics are a soft emphasis. Links generally need a stronger "emphasis" to make them stand out. Don't take this as advice to bold all your links, mind you; they don't need too much emphasis either. Links should be noticeable as you scan the page, but they shouldn't steal attention like bold text. Too much bold gets very distracting and poor use of it will harm scanability.
I don't see how italics would make links look less like links; italics aren't for links but they don't especially express that something isn't a link either. I would focus on what makes them look like links, not what makes them not look like links. If you want people to recognize links, make them blue; users click blue links more and blue is the standard color of links.
Underlined text, while stylistically troublesome, also suggests a link. From your question it sounds like you're underlining links only on hover? Note that that is a cue that is only visible once the user is already hovering. Does your user have enough of a cue to try a hover action on your links?