The men from the capital missed an opportunity to climb above the Steelers on Wednesday when the sides played out a goalless draw, remaining three points adrift of the final AFC Champions League berth.
That result means the Steelers, who have won just one of their last 11 fixtures, only need a draw against Suwon Bluewings to make sure of their continental qualification, but defeat against the second-placed side could cost them dearly.
Seoul have a better goal difference than their rivals, so a win by any margin at Jeju United on Sunday would be enough to see them go third in the event of a Steelers defeat.
Jeonbuk Motors have long since sealed top spot in the South Korean top flight, but will be keen to finish with a flourish against an Ulsan side who have struggled since the division split in two.
Ulsan have failed to register a victory against Jeonbuk in the last four meetings between the sides.
The battle to avoid relegation stepped up a notch with Seongnam's 1-0 win at Incheon United on Wednesday.
The victory lifted them out of the relegation play-off spot - now occupied by Gyeongnam.
Another win at home to Busan I'Park would guarantee Seongnam's safety for another season, but Gyeongnam will not have given up hope of reeling in the Korean FA Cup winners.
They head to Sangju Sangmu, whose relegation to the second tier after a one-year stay in the top flight has already been confirmed.
Incheon are not quite assured of safety just yet, either, although it would need a seven-goal swing between themselves and Gyeongnam to see them potentially dumped into the bottom two.
Jeonnam Dragons host Incheon, guaranteed to finish top of the bottom half.
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