The 21-year-old midfielder-cum-leftback has made only a handful of appearances since coming through the club's youth system, and enjoyed a six-game loan spell at Cambridge United last season.
His chances of making City's first team this season look just as slim with both Andy Dawson and Roland Edge ahead of him for the left-back spot. He may therefore be interested in going to the League Two side to play first team football.
Alexander told the Lincolnshire Echo: "I want to bring in the lad on loan for the whole season if I can. I am busy negotiating the deal and it is now a case of waiting for people to get back to me with an answer.
"I've seen Nathan a few times for Hull's reserves and I believe he can do a good job for us.
"We only have a couple of left-sided players at the club with Peter Gain and Kevin Sandwith, and we haven't replaced Mayo yet.
"Hopefully Nathan will help us for one season, at least."