Specially trained officers who liaise with other agencies to provide support during any investigation are available to help, detective chief inspector Sarah Taylor said.
The call comes as it was revealed that allegations of abuse have been made by former players across the UK. Police Scotland said 298 crimes have been recorded so far in their investigation into football-related sexual abuse.
Police said there were 167 instances of people giving information about historical sex abuse.
Everyone who reported abuse or provided information has now been contacted by the force.
The Scottish Football Association (SFA) has set up an independent review tasked with examining child protection “processes and procedures” in place both currently and historically in Scottish football.
DCI Taylor said: “While the single investigation into those named during our inquiries has concluded, we appreciate how difficult it can be to report abuse.
“We want to thank everyone who came forward and reported, we understand the courage it took and how difficult this must have been. Our assurance to anyone who has not felt able to report during this time is that if they wish to report in the future, we will listen; we will investigate regardless of where or when the abuse occurred, and we will take prompt action to ensure that no-one else is at risk of harm.”
“Police Scotland has dedicated, highly-trained and specialised officers, who work closely with other agencies to ensure that support and advocacy services are available to meet individual needs, during investigation.
“We would ask anyone who has concerns or information about any person who may pose a risk to children or who may have abused a child to contact Police Scotland.”
Scotland’s former Children and Young People’s Commissioner, Tam Baillie, described the “power imbalance” between the football clubs and the children involved.
“The children have got dreams of being football players, the clubs are their access to those dreams and that really creates a very big power imbalance. There has to be acknowledgement of that.
“My call is for the governing bodies [the SFA and the Scottish Professional Football League] to take the power imbalance much more seriously and demonstrate that they will listen to children and respect children’s rights.”
An NSPCC Scotland spokesman said the figures from Police Scotland confirmed the “deeply disturbing extent” of the abuse that had taken place within football.
He added: “The NSPCC’s own dedicated football abuse helpline has itself received more than 2,500 calls from across the UK since this scandal began.
“It’s vital that victims feel safe to come forward and that all allegations of abuse in Scottish football are thoroughly investigated.”