Sexwale and his office were not immediately available for comment.
But an unnamed executive committee member of the South African Football Association (SAFA) told the local Sunday Times weekly that “we have been told that he is not taking the African continent seriously.”
“And just about everybody on the continent says he must withdraw from the presidential race,” said the official.
The City Press, another South African Sunday paper also cited an unnamed SAFA official saying the business tycoon may be dropped if he did not get CAF’s backing on February 5.
There has been huge criticism regarding the campaign of Sexwale, the only African candidate bidding for the job.
The bosses of the football associations of Namibia and Zimbabwe also voiced concern at Sexwale’s campaign tactics.
“We are in the dark and we do not know as neighbours what his strategies are. Maybe they do not need our vote,” Namibia’s Football Association president Frans Mbidi told the Sunday Times.
Zimbabwe Football Association’s president Phillip Chiyangwa was also quoted by the Sunday Times saying: “South Africa and their candidate are not doing good enough to enlist our support”.
Last week Sexwale said the next FIFA leader must come from Africa or Asia and that he was ready to form an alliance to stop a European candidate.
“I am focused on making sure that the president of FIFA comes from either Africa or Asia, not Europe,” Sexwale told South Africa’s Metro radio on Thursday.
Sexwale, an anti-apartheid prisoner with Nelson Mandela who became a businessman and politician, also raised the possibility of some candidates joining forces.
“The time for alliances is… coming, and it’s healthy, it’s democratic and it’s good,” he said. “Now we are talking… we are brothers, we are colleagues.”
He did not name his allies, but the Asian Football Confederation (AFC) this month signed a cooperation accord with the CAF.
Sheikh Salman bin Ebrahim al Khalifa, head of the AFC and a member of the Bahrain royal family, is considered one of the frontrunners in the race to replace the suspended Sepp Blatter.
He is up against Jerome Champagne, a French former FIFA official, UEFA general secretary Gianni Infantino, South Africa’s Sexwale and Prince Ali bin al Hussein of Jordan.