Veivers, 48, was sacked by the City Reds earlier this season following a turbulent off-season, and has previously served as assistant coach at Bradford and Wigan, ironically to new Reds coach Brian Noble.
The Australian, a full-back in his playing days, has been in this country since he left Queensland for St Helens back in 1984, spending 12 years at Knowsley Road and also playing for Huddersfield.
He said: "I’ve been away from the game for a few weeks, so I’m really looking forward to working with Brian and putting one over on England.
"We’ve named a strong squad, and part of my role will be to keep an eye on the players we’ve already named and those who are keen to break into it. There are plenty of outstanding players who haven’t been named and the door is still open."
McClennan last week named a 27-man squad, to be captained by Warrington's Brett Hodgson, for the game at the Halliwell Jones Stadium on Friday June 14.
The Rugby Football Union say they will not stop Sale signing Castleford winger Denny Solomona.
RFL chief executive Nigel Wood as thrown his support behind England coach Wayne Bennett, saying the Australian has "challenged the sport in this country" to be better.
RFL boss Nigel Wood says the situation involving Castleford winger Denny Solomona is a concern for more than just rugby league.
Catalans Dragons have signed prop Paul Séguier and hooker Alrix Da Costa on full-time contracts.
Widnes captain Kevin Brown has signed a two-year deal with rivals Warrington.