The BBC has learnt lock Joe Launchbury and centre Jonathan Joseph are both in danger of being shock exclusions from Warren Gatland's squad.
England captain Dylan Hartley's chances are rated as 50-50, but about 14 Englishmen are expected to be included.
Rookie prop Kyle Sinckler and centre Ben Te'o look likely to make the cut.
Head coach Gatland is set to name his squad of 37-39 players at midday on Wednesday.
Gatland and his coaches will meet for a final selection meeting on Tuesday, with Lions sources insisting nothing is yet set in stone.
Wasps forward Launchbury, 26, was short-listed for Six Nations player of the tournament, but is part of a fierce competition for places in the second row.
With Alun Wyn Jones and Maro Itoje certainties to make the touring party, Launchbury is believed to have slipped below compatriots George Kruis and Courtney Lawes in the Lions pecking order, while Gatland is understood to be a supporter of the Irishman Donnacha Ryan.
Joseph has been tipped by many pundits to start the Test series at outside centre, but Gatland's preference for size in the midfield could see the likes of Te'o and Wales' Jonathan Davies preferred.
Meanwhile, despite captaining England to back-to-back Six Nations titles, Hartley is struggling to force his way into the squad as one of the three hookers, with Ireland's Rory Best and Wales' Ken Owens vying for places along with England second-choice Jamie George.
Other England stalwarts such as flankers James Haskell and Chris Robshaw, as well as fly half George Ford, also thought to be unlikely to force their way into Gatland's plans at this stage.
The tour begins on 3 June and features a 10-game schedule, culminating in a three-Test series against the All Blacks.
The Lions will be looking for a second series win in New Zealand, with their only triumph to date a 2-1 victory in 1971. - BBC -