The Australia-born former St Helens centre was sacked by new Salford City Reds owner Marwan Koukash five rounds into Super League XVIII and jumped at the chance to help McClennan plot the downfall of England in the International Origin match at Warrington on June 14.
"To be back involved in the game with the Exiles is great," Veivers said. "I think I've been out of the game seven weeks and it's probably been the hardest seven weeks in the sense that I've been looking at four walls every day rather than working a 60 or 70-hour week."
Veivers, 48, who has been involved in the English game for almost three decades, helped the Auckland-based McClennan select a 28-man squad and will keep a check of the form and fitness of candidates until the former New Zealand boss arrives to take full charge.
"It came out of the blue," Veivers added. "I was sat in one evening and he rang me up and asked me to assist him.
"I'll be his eyes and ears because the only games he's going to get over there are the ones that are on Sky whereas I can see every game and keeps tabs on how the players are going.
"We've got a 28-man squad but it's not a closed shop. Anyone who is outstanding from outside that squad has a chance of breaking in. There are near enough 90 overseas players still running around in Super League that we can tap into. I think we've assembled a pretty skilful and big and fast side."
Warrington full-back Brett Hodgson has retained the captaincy and is joined in the squad by club-mates Joel and Michael Monaghan and Trent Waterhouse. St Helens also have four representatives and would have had five but winger Francis Meli has been ruled out through injury.
Exiles squad: Louis Anderson, Daryl Millard, Zeb Taia (all Catalan Dragons), Chris Bailey, Antonio Kaufusi (both London Broncos), Michael Dobson, Mickey Paea, Cory Paterson (all Hull KR), David Faiumu (Huddersfield), Blake Green, Pat Richards (both Wigan), Rhys Hanbury (Widnes).
Brett Hodgson (capt), Joel Monaghan, Michael Monaghan, Trent Waterhouse (all Warrington), Lance Hohaia, Willie Manu, Tony Puletua, Iosia Soliola (all St Helens), Kylie Leuluai, Joel Moon (both Leeds), Heath L'Estrange, Manase Manuokafoa, Jarrod Sammut (all Bradford), Mark O'Meley (Hull), Justin Poore (Wakefield).