The national coach will name his first squad on Tuesday since being announced as Wayne Bennett’s successor last month and the uncapped in-form duo are understood to feature.
McShane, 30, fully deserves his call-up after being one of the best nines in Super League in recent years.
Many thought the former Leeds Rhinos player should have earned a Test cap in 2017 having been inspirational as Castleford came top for the first time in their history and reached a maiden Grand Final.
He was included in Bennett’s initial elite performance squad but never made the cut for the World Cup and has not been involved at all since, although with Josh Hodgson, James Roby and Daryl Clark in front, England have not been short of quality hookers.
However, after another excellent start to this season, Leeds-born McShane is clearly in Wane’s thoughts ahead of the Ashes series at the end of the year and could finally get that chance.
Similarly, Griffin has been outstanding for Hull so far this term, backing up his excellent 2019 club player of the year form.
No one has made more metres or tackles busts in Super League and the 29-year-old has been terrorising defences, marking out his international potential.
Elsewhere, Huddersfield Giants captain Aidan Sezer has avoided a ban for the high tackle on Thomas Leuluai that led to such a costly spell in the sin-bin against Wigan Warriors on Sunday.
The Australian scrum-half was charged with a Grade A high tackle by the match review panel but received a zero match penalty notice so is free to play when Giants visit St Helens on Friday.
However, in-form prop Suaia Matagi has been hit with a one-game ban for a Grade B trip in the same match so misses the fixture.
Saints, too, will be without one of their players after hooker Aaron Smith was suspended for a match following a Grade A dangerous contact in their win over Toronto Wolfpack.