Sundowns signed the Bafana Bafana centre-back on transfer deadline day in August from Ajax Cape Town following his aborted move to Glasgow Celtic.
Coetzee was denied an overseas switch after failing his medical at the Scottish giants due to an underlying problem in his right foot.
It was initially thought the 20-year-old needed an operation, but Downs spokesman Thulani Thuswa says this is no longer the case.
"It doesn't look like there will be any surgery," says Thuswa.
"Everything else is going well with his progression with his recovery."
Thuswa says Coetzee is expected to be out of his moon boot in a "couple of weeks".
Fellow casualties Anthony Laffor (foot) and midfielder Oupa Manyisa (groin) will also be assessed today.
"Anthony Laffor was carrying a knock. He will be checked with how far he is with his recovery. Also remember there was the international break. Every time they come back, they are coming back today, all of them, they get checked for knocks. But so far there is no major concerns."
He adds: "Oupa Manyisa was also with an injury; he's also to be checked today with how far he is."
Recently promoted starlet Keletso Makgalwa marked his return from injury by scoring a last-gasp winner in a 3-2 win over Kaizer Chiefs in the MultiChoice Diski Challenge on the weekend.