Albion are being frustrated by the Premier League’s bottom side with Clarets keeper Nick Pope the man of the match so far.
Danny Welbeck had has a couple of chances including a one-on-one with Pope.
Tariq Lamptey had a great chance earlier on but fired high and wide when well placed.
Adam Webster and Pascal Gross have also had chances to put Albion in front as Adam Lallana pulls the strings in midfield.
Matt Lowdown hit the bar from a cross-cum-shot and Robbie Brady, with an ambitious overhead kick, also went close for Burnley.
But the visitors have offered very little else so far.