The Bafana Bafana international re-established himself as one of the top strikers in the Premier Soccer League (PSL) during the 2019/20 season.
City chairman John Comitis revealed that they have had talks with Sundowns, but they are waiting for the reigning PSL champions to make an offer for the player.
“Sundowns showed interest about three weeks ago," Comitis told IOL.
"They spoke to me but nothing has materialised since then. At the moment, we’ve heard nothing from them."
Erasmus, who netted 13 goals in the league, played an instrumental role in helping Citizens finish sixth on the PSL standings and they qualified for next season's MTN8.
Comitis indicated that they are open to selling the former Orlando Pirates centre-forward, who helped the Buccaneers finish as runners-up in the 2015 Caf Confederation Cup.
“We have to be realistic about Kermit’s value," the former Ajax Cape Town chairman said.
"If we get a realistic value for his services we have to entertain it [the interest] because we have a plan on how to cover the void that he will leave if we agree a deal with Sundowns."
Erasmus is an experienced player having turned out for several clubs in Europe, including Dutch giants Feyenoord, French sides Stade Rennais and RC Lens, and Portuguese club Vitoria Setubal.
Comitis also confirmed that there is an overseas club keen on the Port Elizabeth-born player, while Thamsanqa Mkhize has also attracted interest from an unnamed team.
However, the experienced administrator is not prepared to lose City's captain Mkhize, who has been with the club since its formation in 2016.
“[Yes], I’ve also got an international interest for him, but at the moment nothing has happened. There was also interest for one of our defenders [Thami Mkhize]," he revealed.
"We are not entertaining that, we’ve got a team put together to challenge for things."
Mkhize, who is also a former Pirates player, has been linked with Sundowns in the past, but City managed to retain his services.
The 32-year-old played 28 matches across all competitions for the Citizens in the recent season.