Police have cordoned off a house in Martyrs Avenue, Langley Green.
Officers from the Counter Terrorism Unit are searching the house as part of investigations into a suspected suicide bomber.
Crawley’s district police commander said officers were working with the South East Counter Terrorism Unit with inquiries into a suicide bombing in Syria.
The bombing was in the Syrian city of Aleppo last week.
A man, believed to be from Sussex, and alleged to have to have been responsible for the attack has been named in some reports and on social media.
Sussex Police Chief Inspector Justina Beeken said: “There has been social media posts which we are aware of and we held a meeting to reassure and engage with the community in Crawley regarding these.
“There has been no formal identification of the man and therefore we cannot confirm who he is or where he is from.
“Sussex Police are closely liaising with the South East Counter Terrorism Unit in relation to its enquiries.
“We are supporting communities in Sussex and are asking anyone with concerns about the situation to speak to officers by dialling 101 or email firstname.lastname@example.org.”
Updates to follow.