A well-placed source said both clubs agreed on the transfer on Sunday for the former Bloemfontein Celtic player to make the switch from Cape Town to Pretoria.
"It’s just a matter of reaching personal terms but the deal is a formality," said the informant.
Sundowns spokesman Thulani Thuswa was tight-lipped when contacted for comment. He said: "I don't know about this."
This website has been informed that Bidvest Wits were favoured to clinch Lakay's signature until the Brazilians made a late charge for the 26-year-old's services.
Lakay, who made 35 appearances in all competitions in 2017/18, joined City on a deal that runs until 2020 at the beginning of last season from Celtic.