The Irishman arrived from Blackburn in August 2011 and is out of contract at the end of the season.
The Tangerines have recently extended the contracts of Ryan Gauld, John Souttar, Andrew Robertson, Nadir Ciftci and Stuart Armstrong, and Gunning believes he will be next.
"I have been weighing my options up and if we can get something sorted then great," the 22-year-old told the Daily Record.
"I have a lot of things to consider but it's definitely an option.
"These are exciting times to be at United, you just have to look at what's on the pitch to know what these boys are capable of."