AmaTuks have struggled recently – after making an impressive start to their debut season in the Premiership the University side haven't managed to win a game this year.
Barker, however, is positive of his side's chances of finishing in the top half of the table. Tuks are currently in ninth, two points behind Maritzburg United.
"It may be a bit of a cliché answer but we want to finish as high as possible, and we don't know where that is. It could be top eight, it could be top 10, it could be top 12 – we just want to finish as high as possible.
"And for me we are only six points off fourth position so if we finish off strongly finishing of in the top eight is possible."
But Barker adds that his side's number one priority is to ensure they gather enough points to be safe from relegation.
AmaTuks are only 10 points above last placed Chippa United, with nine games still to be played this season.
"Our number one priority is to ensure that we get enough points until we are as safe as possible. Once we achieve that objective, we can focus on finishing in the top eight.
"The first objective is to get points on the board so we don't have to keep looking over our shoulder," Barker says.
AmaTuks face Soweto giants Orlando Pirates at Soccer City on Saturday.