Chelsea and Manchester City resume their Champions League campaigns this week with Manchester United and Wolverhampton Wanderers also continuing in the Europa League.
Lampard’s injury-plagued Blues have a 3-0 deficit to overturn in their last-16 second-leg fixture at Bundesliga champions Bayern Munich on Saturday.
Even if they fail in the match, they will have just 35 days before the new Premier League season starts.
“I would like to think the Premier League would look seriously at that,” Lampard said when asked about the scheduling of fixtures.
“Hopefully they give us a fair start next season. Even in a worst-case scenario, we don’t go through against Bayern, the 12th feels too early for me for the players to start playing again.”
It remains likely that the Premier League will accept requests from teams involved in UEFA competitions for a staggered start to their opening fixtures of the 2020-21 season.