They agree with the concept but early rounds of the competition clash with international Under-21 games.
Arsenal, Tottenham and Chelsea, Manchester United and Liverpool are all expected to decline the chance too.
But Southampton, Stoke, Sunderland and Swansea are among the clubs who will accept their invitation.
Manchester City's under-18s have reached the final of the FA Youth Cup for the last two years - losing to Chelsea on both occasions
The Football League spoke to the Premier League before revealing their expansion idea last week.
Up to this season, the competition had been reserved for League One and League Two clubs.
Barnsley beat Oxford United in last season's final at Wembley.
An EFL spokesman said: "The EFL is currently awaiting responses from a number of clubs that have been invited to take part in this season's EFL Trophy. Already a number of clubs have accepted our invitation.
"In any instances where clubs do decline, we will issue invitations to other clubs with category one academies in the order in which they finished in the 2015/16 domestic league tables."