The world governing body has informed the Sao Paulo club that there will be no extension of the December 2013 handover deadline but will look to work with them to stay on schedule
The Arena Corinthians is under construction ahead of next year's tournament, but Fifa general secretary Jerome Valcke warned earlier this week that World Cup fixtures scheduled to take place at the Sao Paulo venue could be switched to another city if Fifa is not confident the stadium will be ready in time for the December 2013 handover deadline.
On a visit to the Mane Garrincha stadium in Brasilia, Valcke stated: "We have always said that delays cannot be accepted. It takes time to test everything and the World Cup is an event of huge magnitude.
"[Corinthians] will have to accelerate. This is not a threat. We are not thinking of changing the host city as this only happens when there is no other way.
"But we can change at any time before August 1, when ticket sales will begin. We have a chance to do that, but the stadiums must be ready on time."
Corinthians hit back in a prepared statement, saying they would not be pressured by Fifa and would be understanding should the world governing body feel the need to change venues for Sao Paulo's allocated matches.
"Corinthians started the works almost a year after the other stadiums, and even with all the difficulties with the financial transfer of funding and delays by the construction company Odebrecht, the building is going to plan," read the club's statement.
"Work is already 76 per cent complete, and the club finds it strange that Mr Valcke took such a position on Tuesday, especially in stating the December 2013 deadline. For Corinthians, the deadline was extended by Mr Valcke himself to February 2014.
"The club accepts no pressure... if they feel they must change venue, we understand and are comfortable. Corinthians just hope Fifa and the Local Organising Committee (LOC) recognise the effort of the Municipality of Sao Paulo, the State Government, the Federal Government, and especially the people of Sao Paulo."
Fifa's response has been to confirm that talks will take place regarding the present discourse.
Speaking to Goal, a Fifa spokesperson confirmed: "The deadline for the delivery of all stadiums for the 2014 Fifa World Cup is a firm December 2013. Fifa acknowledges the statement released by Corinthians.
"As said yesterday [Tuesday] by Fifa secretary general Jerome Valcke, there will be meetings between Fifa, the LOC and the club to address the mentioned matters and discuss solutions."
The latest concerns over the Arena Corinthians come just a matter of days after it was confirmed that substitutes benches at all 12 World Cup stadiums will need to be realigned to fit with Fifa regulations, including six to be used at June's Confederations Cup.