Compensation in the salary cap for clubs that commit players to England.
"Moving the Powergen Cup to pre-season would enable England players to have a good rest because they would not have to play in it," said Connolly.
"The average English player that tours in June is under pressure from his club to come back straight away but this way they could get their two to three months off."
According to Connolly, the move would also help sides that contribute players to the international team.
That is because the Premiership fixture list could be rejigged so less league games clash with international weekends.
"There are only four or five clubs providing all the players for England and that is not in anyone's interest," said Connolly.
"We are delighted to have players in the England squad but the downside is that when you hit November you are disadvantaged terribly.
"There are four or five clubs that don't sign people who are going to play international rugby. I can understand that.
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I have had a wonderful time and it is very hard to leave Bath
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"With relegation involved, one slip you can be out of the door. Having players unavailable for so much of the season has huge ramifications."
Connolly also says the ongoing conflict between the clubs and the Rugby Football Union has to be resolved if England are to repeat the World Cup final glory of 2003.
The two parties are locked in a long-running dispute over training access to England players.
"Lessons could be learnt from when England won the World Cup in 2003," said Connolly. "There was a great preparation for England and we saw the result of it.
"Balancing England's ambitions with the lifeblood of the game - the clubs and the supporters - is the challenge.
"Both parties have to give a bit and respect the other in terms what they are trying to achieve.
"After all, they are trying to achieve the same thing, which is better rugby players and an England win at the next World Cup."
Connolly, who is being replaced by Brian Ashton at Bath, is looking forward to a break after almost 20 years in the game, although he has not ruled out a return to England in the future.
"I have had a wonderful time and it is very hard to leave Bath," he said.
"But I have spent over five years in Europe and it is time to have a break. It is not about going anywhere else.
"There are no plans just yet, nothing is ruled out or ruled in."