As talks with potential buyer Dr Marwan Koukash, the St Helens-based multi-millionaire racehorse owner, continue to progress, Veivers has expressed his optimism that the cash-strapped club can be saved.
"I've had a chat to see where we're at," Veivers told Press Association Sport. "I don't want to reveal some of the stuff we spoke about. I'm not counting my chickens but I'm very positive there's going to be a positive outcome."
Koukash, owner of global executive training company EuroMaTech, flew back from Dubai earlier this week to hold talks with development company Peel Holdings and Salford Council, the joint landlords of the Salford City Stadium, who are both keen to keep the ailing club afloat.
A further meeting was held at the stadium on Thursday morning between outgoing club chairman John Wilkinson, RFL chief executive Nigel Wood and former chairman of New Zealand Rugby League Andrew Chalmers, who is expected to play a role in the new management.
It is thought a deal could be completed within days, which would be a major relief for Veivers, who has endured a traumatic pre-season.
"I'd be a liar if I said it had run smoothly," he said. "What I can say is that the players have rolled their sleeves up got and stuck in.
"Obviously there's been some blips when the players have had down days, wondering whether they're going to have a job or not.
"It's been very tough. I've had the same fears as the players but we've had to be there to pick them up.
"Through the whole pre-season, there's probably only been one day when I was deflated and felt the worst. I went home and said to the wife I needed to sort myself out. It wasn't something I needed the players to see."