The government wants to offer rail season ticket holders a "free week" in the wake of criticism of services.
ScotRail boss Phil Verster told MSPs talks are ongoing over how the plans will work and how they can be funded.
He said he had been told to use money from a rail improvement fund already earmarked for other projects, and "couldn't vouch" for it going ahead.
The Scottish government said it "remains absolutely committed" to the initiative.
The Â£3m scheme was announced as part of the Scottish government's draft budget, in a move to compensate passengers after a series of delays and disruptions on the rail network.
Appearing before MSPs on the rural economy and connectivity committee, Mr Verster said he first heard of the project "two to three weeks" before Transport Minister Humza Yousaf announced it.
He told members there were plans to use Â£1.8m from the Service Quality Incentive Regime (Squire) railway improvement fund, which is controlled by Abellio ScotRail alliance and built up through fines and penalties imposed for delays and other infractions.
The cash had already been earmarked for "other initiatives".
SNP MSP Christine Grahame asked Mr Verster if the firm, as a private company, could tell the government "you're not having it" over the Squire cash.
He told her: "We are busy discussing this with Transport Scotland and I prefer not to commit to a position yet."
Ms Grahame said: "So the scheme might not go ahead because you've not decided 'Yes, we're going to do this'?"
Mr Verster replied: "I can't vouch for whether the scheme goes ahead or not. I can just comment on whether we will make that decision, and when we'll make the decision in the next couple of weeks in terms of how we will deploy the Squire fund."
He said talks were ongoing about how the scheme would be funded, and said he had not thought of using the Squire money until it was suggested by the government.
Labour MSP Rhoda Grant said: "This is quite extraordinary. I was going to say this is policy made on the back of a fag packet, but I don't think it's even reached that stage of development."
Liberal Democrat MSP Mike Rumbles said he had assumed the Scottish government would be paying for the free fares scheme.
He said: "It's not new money that the Scottish government is using, it's money that you were going to invest in the railways."
He said it was "completely inappropriate" for the transport minister to ask for the money and it should up to Abellio ScotRail how to spend it, not the government.
Mr Verster replied: "We have a very constructive relationship with Transport Scotland and the Scottish government. A very open relationship.
"Now while we set may priorities of what we think would be best for customers, if Transport Scotland engages with us and makes alternative suggestions, of course we consider that.
"I don't think there's anything inappropriate about that. I think what is important is only one thing and that is customers in the end."
Mr Yousaf was also originally scheduled to give evidence to the committee, but this was postponed as he was unwell.
A spokesman for the Scottish government said it "remains absolutely committed" to the scheme.
He said: "A free week's travel will be offered this year and further discounts for daily, weekly and leisure travellers.
"The ScotRail contract permits Squire funding to be directed to initiatives that improve the customer service experience, and we are currently negotiating the terms of the fares initiative with ScotRail through Transport Scotland, with the details expected to be finalised and announced in the coming weeks."
A government scheme to compensate rail passengers with free tickets may not go ahead unless it is fully funded.