The tournament was initially scheduled to take place in Cameroon, but Caf decided to take those rights away from them following delays in construction of stadiums.
Caf then announced that African countries wishing to bid for the 2019 Afcon finals have until the end of December to submit their bids.
According to reports, Morocco and South Africa are strong favourites to take over from Cameroon.
While Safa communications head Dominic Chimhavi told Goal on Saturday afternoon that the possibility of bidding to host next year's Afcon had not been discussed by the association, Jordaan told Safa's annual general meeting (AGM) on Sunday that they have been requested to consider hosting the tournament.
Jordaan joined the Safa AGM in Sandton on Sunday morning soon after returning from Ghana where Caf's Extraordinary Executive Committee took the decision to strip Cameroon of the hosting rights.
However, Safa said that they will first have to meet with the South African government to discuss the matter before making a decision.
SAFA President has told the SAFA AGM in Sandton on Sunday, 2 December that CAF has asked the Association to seriously consider hosting AFCON 2019.— Bafana Bafana (@BafanaBafana) December 2, 2018
SAFA will however, meet the Government first before making a decision pic.twitter.com/zofivdFK5A
Meanwhile, Safa vice-president and PSL chairman Dr Irvin Khoza strongly believes that the association should submit the bid to Caf, adding that this will ensure that South Africa remains a major role player both continentally and globally.
SAFA Vice President & PSL chairman Irvin Khoza has urged SAFA to make the 2019 bid as it is important for SA to remain a major role player continentally & globally.— Bafana Bafana (@BafanaBafana) December 2, 2018
AFCON will help in building influence & relevance, added Dr Khoza. pic.twitter.com/4Z0klaJlHW
South Africa last hosted the continental showpiece in 2013 after jumping at the opportunity to replace Libya.