Liverpool manager Brendan Rodgers is among those who feel that players should not be chasing moves during the opening games of the season, with the Toffees having tried to fend off Manchester United's pursuit of Marouane Fellaini and Leighton Baines throughout the summer.
Fellaini eventually made the move to Old Trafford on deadline day and Jagielka is eager to avoid similar situations occurring in the future.
|4/1||Everton are 4/1 with BetVictor to finish in the Premier League top six
"I would like it to be moved two weeks earlier so, when you start the season, you know they are the players you have got."
The Premier League side did some business of their own on deadline day, securing the signings of Victor Moses, Gareth Barry and James McCarthy, and the defender is pleased with the late additions.
"The squad has become stronger in numbers but time will tell," Jagielka added. "It looks good and the manager has done well.
"I know Gaz [Gareth Barry] very well and he's a fantastic player and James McCarthy played very well for Wigan last year.
"Hopefully the manager can get us playing how he wants to and we can score some goals to get up the league table."