The transport operator said it intends to bring a judicial review, which is a court proceeding where a judge looks at the lawfulness of a decision or action by a public body, unless the Welsh assembly's plan is reconsidered before April 1.
The potential action comes after the Welsh Government recently agreed a funding package of £189 million for free bus travel in Wales for the next three years.
That is a reduction of more than 11% on the £213.3m that has been allocated during the past three years.
Around 720,000 people in Wales, including serving members and veterans from the armed forces, are eligible to use the scheme.
Stagecoach said its legal advisors suggest the Welsh Government has made an error by capping the scheme to fit within a budget as opposed to following a statutory principle that transport operators should be no better and no worse off as a result of a concessionary scheme.
That principle makes allowances so operators should not miss out on the fares they would have collected while also taking into account the likelihood that more people are likely to travel as a result of a concessionary scheme.
Perth based Stagecoach is the largest bus operator in Wales with seven depots, almost 400 vehicles and around 900 staff.
John Gould, managing director of Stagecoach in Wales, said: "The Welsh Government has so far refused to listen to warnings from bus operators, passengers, public transport campaigners and community groups. Legal action is a last resort and we have written to the Welsh Government to give them an opportunity to re-think their decision. We want to protect people from the devastating impact of these brutal, flawed and unlawful cuts.
"The Government has broken the key-stated principle that bus operators are properly and fully reimbursed for the costs of participating in the mandatory scheme.
"It has effectively rewritten the rules to its own specification and to suit its own purposes while dressing up the changes as the result of an independent review.
"The damage will be felt all across Wales and people are rightly angry."
Stagecoach indicated it may be forced to cut services if the changes to scheme, scheduled to be brought in from July, are introduced.
Mr Gould added: "From housing estates to the high street, the Government's cuts are an attack on daily life in Wales. It will directly lead to significant cuts to bus services. There will be an even wider impact as the fall-out will hit the most vulnerable and affect living standards for the poorest in our communities. Ministers will be collectively responsible for job losses and cutting people off from accessing vital education, employment and health facilities."
Lawyers from Herbert Smith Freehills have suggested to Stagecoach that the Welsh Government has had key failings in the process it followed and may be liable to compensation claims through a violation of European Union law.
Letters from lawyers have also been sent to 10 local authorities in Wales, responsible for operating the concessionary travel scheme, where Stagecoach has routes.
The letters suggest following the Welsh Government's new guidance would not be lawful.
The Welsh Government has reduced its Bus Service Operators Grant by 25% in the past year.
Stagecoach said this has increased the cost of travel for passengers and meant some routes are not viable.
A Welsh Government spokesman said: "The new rate, recommended by an independent review, maintains the principle that bus operators who take part in the scheme are no better and no worse off. Any operator who believes they may be adversely affected by a local authority's reimbursement arrangements have the right to appeal to Welsh Ministers."