The move could spell the end of friendly matches.
Gill, speaking after the European Clubs' Association's (ECA) annual congress in Geneva, said they want to reduce the number of international dates to just 12 over a two-year period, or six a year apart from finals tournaments.
That would mean either much smaller qualifying groups or very few friendly fixtures, or even none at all. Next year there are 11 international dates in the calendar - not including Euro 2012.
Gill, a member of the ECA board, told a news conference the clubs were especially keen to get rid of international friendly dates in June and August.
He said: "In an ideal world, we've been talking about six double-dates over the two-year period.
"It's a reduction but still gives the right balance to the requirements of the national teams and what the clubs want."
Karl-Heinz Rummenigge, ECA chairman and chief executive of Bayern Munich, said the clubs were tired of releasing their players for "nonsense" matches.
Rummenigge added: "We have to come back in favour of quality not quantity.
"When I played in the European Championships in the 1980s there were eight teams, now it is 16 and in 2016 it will be 24.
"The World Cup is similar, from 16 teams to 32 now.
"Everything in the international calendar is balanced in favour of national teams.
"[Qualifying groups] used to have groups of four, now it is six or seven. It has to be stopped that we release players for nonsense dates."
Rummenigge played down suggestions the ECA clubs would break away from FIFA and UEFA if their demands were not met, and backed FIFA president Sepp Blatter to bring in reforms of the world governing body.
"Our goal is not to break away but to find good solutions, not just for clubs, but for football," he added.
"I believe it is good that Blatter announced he is ready for reforms."
Rummenigge said he took back comments he made about Blatter in Swiss magazine Bilanz that he needed to reform "before a revolution comes from outside... [Egypt's president] Mubarak never imagined a year ago that he would be hounded from office".
He said: "I had a call with Blatter and I would like to clarify the meaning, I didn't want to use this aggressive tone. It was not fair to him."