Goal reported on the weekend that Amakhosi were closing in on Lebusa, and that the player was scheduled to undergo a medical at Naturena.
However, the proposed deal has hit a snag, and Ajax are in talks with the Brazilians over the possible transfer of their experienced skipper.
A source within the Chiefs camp confirmed to Goal that it is highly unlikely that Lebusa will join the club, while revealing that Sundowns tabled a better offer to that of the Soweto giants.
"It looks like it's not happening anymore. Lebusa is not coming to Chiefs. The talks were promising just last week, but I hear Sundowns made a better offer to Ajax," the source told Goal.
"So, Chiefs won't make a counter offer. They have decided to look elsewhere. If Sundowns win the race then no issues, but that's the nature of transfer negotiations, and I'm sure they will find the left-back that they're looking for soon," said the source.
Sundowns recently signed Lyle Lakay from Cape Town City to bolster their defence, especially the left-hand side where Tebogo Langerman has been playing.
They also have Siyabonga Zulu, who hasn't enjoyed a fair amount of game time since his January move from Platinum Stars.
Should Lebusa join the 2016 African champions, he will face stiff competition from the abovementioned players, but given the club's hectic schedule, the Welkom-born player would still fancy his chances.
Lebusa is currently in Cape Town, training with the Urban Warriors as they continue to prepare for the new season, although it remains unclear whether they will be campaigning in the PSL or in the National First Division.
Chiefs have missed out on several of their targets in recent years, and their three-year trophy drought is often attributed to their inability to splash cash on quality players.