Earlier, Smith was slapped with one-match ban by the International Cricket Council (ICC) and was also fined for breaching the code of conduct.
Reports said that while Smith and Bancroft have also been barred from captaining Australia for one year after completing their ban, Warner will never be considered for leadership in future. Pressure is being exerted over the chief of Australian cricket team James Sutherland to take strict action against them.
Well-renowned Australian cricket commentator Jim Maxwell said that he thought opening batsman Warner, a divisive figure in the world game, would bear the brunt of the sanctions and was the brains of the ball-tampering plan.
Lehmann, a no-nonsense former player under whom Australia's test side has gained a reputation for pushing the limits of sporting acceptability, would continue in his position under his current contract, Cricket Australia's CEO added.
"The three players on report, we are contemplating significant sanctions, which will reflect the gravity of what has occurred and the damage it has done to the standing of Australian cricket".
The Kiwis, who will be playing England in the Test series hinted that the chillier South Island temperatures could provide Smith with a good way to escape the "heat" back home.
Smith overcame a slow start to his career as a leg-spinning all-rounder to establish himself as the world's number one-ranked Test batsman, and took over the captaincy in 2015.
Prime Minister Malcolm Turnbull said Tuesday it had been "a shocking affront to Australia" and Cricket Australia must act "decisively and emphatically".
"I spoke to people this morning, the players don't want to play the Test".More news: Apple Unveils It's New Cheaper iPad and Offers Schools Discounts
With their heroes being humbled, junior players and their families and friends are having their versions of the "Say it ain't so?" moment.
CA's statement said Warner instructed Bancroft "to carry out a plan to take steps to attempt to alter the condition of the ball using sandpaper".
In addition, all three players will be required to undertake 100 hours of voluntary service in community cricket.
Sutherland said: "The sanctions we have announced are significant for the individuals involved". According to SMH sources close to the dressing room, "the most prominent narrative was that the plan was devised during a discussion between Warner and Bancroft, and that Smith foolishly agreed to it".
Sutherland and his governing body, under pressure from sponsors and in the midst of negotiations over a new broadcast deal, know they have plenty of work to do over the coming months to restore the image of the sport in Australia.
'The key finding is that prior knowledge was limited to three players: Smith, Warner and Bancroft'. As he left the team hotel in Johannesburg, Smith said he didn't feel like playing any cricket right now.
Warner was later named as part of the "leadership group" with Smith at the centre of the decision to execute the tactic.
The evidence from the TV cameras was overwhelming and Smith and Bancroft came out after play to confess to their roles in the plot to reporters.