United have spent £20million on new players already, as Fulham defender Chris Smalling and Mexico striker Javier Hernandez agreed moves to the club earlier this year.
“The money is there if we believe there is a player who can improve what we believe is a very good squad,” Gill told the Manchester Evening News.
“The team has been together for a number of years and done very well. In order to improve it a player has to be of a very high quality.”
“We are always looking at players,” he added. “We are looking 365 days a year – it doesn’t just start when the transfer window opens.
“We are looking at it. We studied a lot of players at the World Cup, but we knew about a lot of them before that.
“Over all I think Sir Alex is very comfortable with the squad composition. That’s not to say something won’t happen, but I think it is a ‘might’, not a ‘will’.
“We will see what happens over the next six weeks.”