A preliminary investigation into Wednesday's accident, in which a crane collapsed and killed two workers, indicated that damage was confined to the concourse area and did not affect the stands - which could have taken longer to fix.
The damaged concourse area took about 35 days to build, and previous experience suggests it will take about twice that time to clear the wreckage and rebuild, the source said. If work resumes on Monday, as the builders believe it will, that puts the completion date in early February.
The source, who spoke on condition of anonymity because the probe into the accident is sensitive and ongoing, expressed "high confidence" in the timeline but said it is subject to change pending further investigation by local authorities.
"The reconstruction is not a difficult thing to do," the source said. "Everyone is mourning the workers, but calm about the construction itself."
If proven true, the news would be a relief for Brazil's troubled efforts to get stadiums and other key infrastructure ready on time before the global soccer tournament opens in Sao Paulo on June 12.
FIFA has said that all of the stadiums to be used for the event must be finished by the end of December.
The source said, however, that FIFA has always been quietly willing to extend the deadline for the Sao Paulo facility - called Arena Corinthians - by a few months if necessary because construction there started a year later than at other stadiums.
"The timeline needed to open the stadium is guaranteed," the source said.
A spokesman for Odebrecht SA, the conglomerate building the stadium, declined comment. Andres Sanchez, a former president of the Corinthians club who is overseeing construction, did not answer phone calls or text messages.
A FIFA spokeswoman told Reuters by email earlier on Thursday that it was "premature" to gauge how long the accident could delay the stadium's opening until next week at the earliest.
The crane collapse was the latest incident to cast a shadow over preparations for the Cup, which have been plagued by cost overruns, delays, and a dramatic downsizing of the public transportation projects that were supposed to be the event's main lasting legacy for Brazil's 200 million people.
Public anger over the billions of dollars being spent on the stadiums boiled over in June, when massive anti-government street protests erupted during a soccer tournament that is a warm-up for next year's event.
Brazilian newspapers said that one of victims of Wednesday's accident, Fabio Luiz Pereira, had dreamed of attending the Cup's opening match at the stadium he was helping build.
The accident occurred as the crane was lifting a large, 420-tonne piece of the stadium's roof into place. It was to be the last of 39 pieces of roof, which is why senior engineers and representatives of the Corinthians team including Sanchez were present when the tragedy took place, the source said.
Photos from the scene show the white, grid-like piece of roof crushed a sizeable section of the facility's exterior.
The initial investigation has identified four possible causes of the accident, the source said. They include the crane breaking due to the roof's weight; crane operator error; a procedural mistake in attaching the roof to the crane; and the crane losing its footing in the ground because of recent heavy rains, which the source said was "very feasible."
One risk to the stadium's revised timeline would be a lengthy legal investigation that freezes construction. However, the Sao Paulo state prosecutor's office said on Wednesday that it would only halt construction if "technical elements warrant."
Odebrecht said on Wednesday it expects to resume building on Monday.
Builders earlier on Thursday ordered a replacement for the fallen piece of roof, a component that is made in Brazil, the source said.
A police inspector also declared on Thursday that he would authorize workers to remove the fallen piece from the scene as soon as possible, the source said.
That development would also suggest a less intrusive approach by authorities to the accident. Sao Paulo's civil police force did not immediately return calls seeking comment.