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.
Wigan's Sean O’Loughlin feels that being in good shape mentally is vitally important to any rugby league player.
Wakefield winger Chris Riley feels that State of Mind has helped to open up players to the prospect of sharing their feelings and not keeping mental issues secret.
Bradford have confirmed that winger Jamie Foster will leave the club at the end of the season.
Winger Danny Williams will make his loan move to Bradford permanent at the end of the season.