Moore has to strengthen his backline after the departure of skipper Ian Sharps, and told The Star of his admiration of Lowton, who last season went on loan to the Blades Hungarian sister club Ferencváros.
The 21 year old can play at Right Back, Centre Back and the right side of midfield.
Moore explained: "Matt Lowton is a player we very much admire and very much like to bring him here on loan.
"But at this stage, all we can do is ask the question and wait for the answer from these bigger clubs. Clubs at the top end of the Championship want to keep their squads intact for pre-season training, and then start to let people leave on loan.
"It's a patience game at the minute; there's nothing we can do. We don't begin pre-season training until July 8, so I imagine a lot of transfer action will begin in early July.
"Hopefully, we can get our back four in place, with some reinforcements, and then build from there. But we were very close to promotion last season, and we've still got 24 players contracted here, so there's no urgent need for players.
"We're not looking for any old player, they have to make our squad better," Moore added. "We're looking at some contract players, but if I find anyone I particularly like I'll have a word with the chairman."