Mowbray's side will be assured of second place at least should Hull City fail to beat Crystal Palace on Saturday.
However, the Baggies boss is not letting thoughts of a first league title in 88 years interrupt his preparation for what could be a vital clash.
"Winning the title has never crossed my mind - it's not a concern," he said.
"Let's do one thing at a time. The objective we've talked about has been to try and finish in the top two.
"If other results get us there this Saturday then great, but if they don't then we have a massive job on Monday for what will be a huge occasion, not just for us, but for Southampton, who could find themselves in the bottom three on Saturday night."