Following their commanding 3-0 win over Golden Arrows at Mpumalanga Stadium, Stellies sit fourth on the table.
Sekhukhune United, who drew 1-1 with Magesi FC, are currently 3rd, just one point ahead.
Barker, who led Stellies to a historic 3rd place and a first-ever CAF Confederation Cup qualification last season, says the race is far from over.
"Yes, it will, it will go to the last game of the season for sure, they are also playing well, they are also picking up results, so you know both teams are applying pressure on each other. So, I do think it will go all the way to the wire," Barker said.
With just three matches remaining in the league, Stellenbosch face a tough test next, away to champions Mamelodi Sundowns at Loftus Versfeld on Sunday, 11 May.
Barker is under no illusions about the challenge but sees it as a key measure of their continental ambitions.
"One of the best teams, if not the best team in Africa. So, we know that whenever we play Sundowns, we have to be at our best, tactically, technically. You have to execute your game plan really well but even if you do that, they've got individual brilliance all around,” he added.
“So, a tough game but we aim to be competitive against Sundowns. We also gotta believe that we can go there and we can get a result if we want to show that we also wanna slowly become a team that's challenging for league titles, being consistently good on the continent. So, it's this type of team like Sundowns that is a good benchmark to see where we are."