Botman has had some shaky moments in Newcastle's back four, which conceded nine Premier League goals across the opening five matches, and his position could come under greater pressure once Burn is available again.
The Dutchman started the 4-1 defeat at Leeds United and was involved in a difficult evening as Dominic Calvert-Lewin caused problems for Newcastle's central defenders.
Jaissle, however, remains convinced that Botman can be an important player for his team.
"I'm fully, fully, convinced about Sven's performances and about Sven as a player as well," the Newcastle United manager said.
"Any player in a season can struggle in a game at times, they are human beings.
"Also they are young. Sven is a big player; he's still a player of huge potential. I am clear his past injuries do not affect him at all. He's fit. He fights for his team."
Jaissle went further when asked about Botman's qualities as a defender, comparing his competitive character to that of a lion.
"He's - how you say in English - a lion. He's a huge cat. We're lucky to have him," he said.
Botman endured a difficult pre-season, with errors in matches against Gateshead, Bristol City and Valencia raising questions over his form before the competitive campaign began.
He nevertheless kept his place for the opening games and produced steadier performances before the problems at Leeds brought the scrutiny back.
Newcastle responded to that defeat with a 2-1 victory over Hull City before the international break, with Botman starting at the heart of the defence.
His continued selection could become a significant decision for Jaissle when competitive football resumes against Coventry City on October 12.
Burn is also pushing for a return after recovering from an ankle injury, meaning Jaissle will soon have another experienced option in central defence.