Maloney said: "I really enjoyed my time at York City, the fans were fantastic, my team-mates made me feel really welcome, and more importantly, it was a great learning experience.
"I enjoyed working under (York boss) Billy McEwan and would be really keen to talk to the club about returning if such an opportunity existed to further my career and help City get back into the League."
United, along with Grimsby and Northampton are interested in the 20-year-old defender, according to the York Evening Press.
All three clubs have invited Maloney for pre-season training but want to monitor him first in July before making any commitment.
Conference North club Harrogate Town and UniBond League first division outfit Guiseley have also made enquiries about the player.
Maloney, who is a student at Leeds University, was released by Doncaster last month after making just four appearances. He came through Rovers' youth ranks.