SBS offered to help the Abbott government in combating radicalisation, but was given a polite "no, thanks".
Managing director Michael Ebeid revealed to a Senate committee on Tuesday that the public broadcaster approached the coalition with proposals before the December 2014 Sydney siege.
"I think SBS is a very important tool that the government should be engaging more with," he said.
"We're a real government asset."
Mr Ebeid pointed to the work done by the broadcaster's radio programs, which air 14 predominantly Muslim languages, and its youth channel.
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There were two or three ideas for programs, including a dedicated Arabic radio program and website.
It would be a place where parents could go to access more information.
"I'm forever hopeful," he said, noting the broadcaster may have been ahead of the times in its offer.
"Some of these initiatives might now have more resonance and be more accepted."
The broadcaster will be holding follow-up meetings with Assistant Multicultural Minister Concetta Fierravanti-Wells later this week.
Communications Minister Mitch Fifield agreed SBS was a force for community cohesion and said he was happy to explore options for an increased role.
The broadcaster met with security agencies about a year ago, but hasn't touched base in the past six to 12 months.
Mr Ebeid conceded they probably should re-engage again.
