The revelation follows Sir Alex Ferguson's stating that the club wouldn't be bringing in any more transfers before the Community Shield meeting with Manchester City on August 14.
“We're looking at one more player to bring in,” Sky Sports quotes chief executive Gill as saying. "Nothing's happening - nothing imminent - on that at the moment, but we'll see what happens when we get home.
"There'll still be 31 days of the transfer window to see if anything develops. But I'm not working on anything at the moment, in that respect."
Since the departure of veteran Paul Scholes, United have been rumoured to be interested in the likes of Arsenal’s Samir Nasri and Tottenham playmaker Luka Modric as replacements.
Inter Milan star Wesley Sneijder has also been linked to a move to Old Trafford, but Gill is refusing to name their wish list.
"We've been looking at a particular position and two or three players in that position, but nothing's imminent at the moment,” he added.
"The important point to understand, and Alex has made it clear, is that we need someone who's going to improve the quality of the squad.
"We've got a great squad and to get into that squad you need to be a world-class player. There's no point, if you can't get the players you want, in buying someone for the sake of buying someone.”
The 53-year-old has insisted that the Premier League champions are in no rush to sign their final addition.
"There's often movement in August. I'm not sitting here saying I'm working on anything specific because I'm not, but that situation could change quickly when we get back to Carrington."
The Red Devils have brought in Phil Jones, Ashley Young and goalkeeper David de Gea to Old Trafford this close season.